Symbolic dynamics and renormalization of non-autonomous k periodic dynamical systems

The purpose of this paper was to introduce the symbolic formalism based on kneading theory, which allows us to study the renormalization of non-autonomous periodic dynamical systems.

Topological Complexity and Predictability in the Dynamics of a Tumor Growth Model with Shilnikov's Chaos

Dynamical systems modeling tumor growth have been investigated to determine the dynamics between tumor and healthy cells. Recent theoretical investigations indicate that these interactions may lead to different dynamical outcomes, in particular to homoclinic chaos. In the present study, we analyze both topological and dynamical properties of a recently characterized chaotic attractor governing the dynamics of tumor cells interacting with healthy tissue cells and effector cells of the immune system. By using the theory of symbolic dynamics, we first characterize the topological entropy and the parameter space ordering of kneading sequences from one-dimensional iterated maps identified in the dynamics, focusing on the effects of inactivation interactions between both effector and tumor cells. The previous analyses are complemented with the computation of the spectrum of Lyapunov exponents, the fractal dimension and the predictability of the chaotic attractors. Our results show that the inactivation rate of effector cells by the tumor cells has an important effect on the dynamics of the system. The increase of effector cells inactivation involves an inverse Feigenbaum (i.e. period-halving bifurcation) scenario, which results in the stabilization of the dynamics and in an increase of dynamics predictability. Our analyses also reveal that, at low inactivation rates of effector cells, tumor cells undergo strong, chaotic fluctuations, with the dynamics being highly unpredictable. Our findings are discussed in the context of tumor cells potential viability.

High Performance Multi-Standard Architecture for DCT Computation in H.264/AVC High Profile and HEVC Codecs

A new high performance architecture for the computation of all the DCT operations adopted in the H.264/AVC and HEVC standards is proposed in this paper. Contrasting to other dedicated transform cores, the presented multi-standard transform architecture is supported on a completely configurable, scalable and unified structure, that is able to compute not only the forward and the inverse 8×8 and 4×4 integer DCTs and the 4×4 and 2×2 Hadamard transforms defined in the H.264/AVC standard, but also the 4×4, 8×8, 16×16 and 32×32 integer transforms adopted in HEVC. Experimental results obtained using a Xilinx Virtex-7 FPGA demonstrated the superior performance and hardware efficiency levels provided by the proposed structure, which outperforms its more prominent related designs by at least 1.8 times. When integrated in a multi-core embedded system, this architecture allows the computation, in real-time, of all the transforms mentioned above for resolutions as high as the 8k Ultra High Definition Television (UHDTV) (7680×4320 @ 30fps).

Makespan computation for GPU threads running on a single streaming multiprocessor

Graphics processors were originally developed for rendering graphics but have recently evolved towards being an architecture for general-purpose computations. They are also expected to become important parts of embedded systems hardware -- not just for graphics. However, this necessitates the development of appropriate timing analysis techniques which would be required because techniques developed for CPU scheduling are not applicable. The reason is that we are not interested in how long it takes for any given GPU thread to complete, but rather how long it takes for all of them to complete. We therefore develop a simple method for finding an upper bound on the makespan of a group of GPU threads executing the same program and competing for the resources of a single streaming multiprocessor (whose architecture is based on NVIDIA Fermi, with some simplifying assunptions). We then build upon this method to formulate the derivation of the exact worst-case makespan (and corresponding schedule) as an optimization problem. Addressing the issue of tractability, we also present a technique for efficiently computing a safe estimate of the worstcase makespan with minimal pessimism, which may be used when finding an exact value would take too long.

Symbolic fractional dynamics

Fractional dynamics reveals long range memory properties of systems described by means of signals represented by real numbers. Alternatively, dynamical systems and signals can adopt a representation where states are quantified using a set of symbols. Such signals occur both in nature and in man made processes and have the potential of a aftermath as relevant as the classical counterpart. This paper explores the association of Fractional calculus and symbolic dynamics. The results are visualized by means of the multidimensional technique and reveal the association between the fractal dimension and one definition of fractional derivative.

Efficient computation of min and max sensor values in multihop networks

Consider a wireless sensor network (WSN) where a broadcast from a sensor node does not reach all sensor nodes in the network; such networks are often called multihop networks. Sensor nodes take individual sensor readings, however, in many cases, it is relevant to compute aggregated quantities of these readings. In fact, the minimum and maximum of all sensor readings at an instant are often interesting because they indicate abnormal behavior, for example if the maximum temperature is very high then it may be that a fire has broken out. In this context, we propose an algorithm for computing the min or max of sensor readings in a multihop network. This algorithm has the particularly interesting property of having a time complexity that does not depend on the number of sensor nodes; only the network diameter and the range of the value domain of sensor readings matter.

Music and evolutionary computation

This paper presents a brief history of the western music: from its genesis to serialism and the Darmstadt school. Also some mathematical aspects of music are then presented and confronted with music as a form of art. The question is, are these two distinct aspects compatible? Can computers be of real help in automatic composition? The more appealing algorithmic approach is evolutionary computation as it offers creativity potential. Therefore, the Evolutionary Algorithms are then introduced and some results of GAs and GPs application to music generation are analysed.

On the numerical computation of the Mittag-Leffler function

Recently simple limiting functions establishing upper and lower bounds on the Mittag-Leffler function were found. This paper follows those expressions to design an efficient algorithm for the approximate calculation of expressions usual in fractional-order control systems. The numerical experiments demonstrate the superior efficiency of the proposed method.

Symbolic dynamics and big bang bifurcation in Weibull-Gompertz-Fréchet's growth models

In this paper, motivated by the interest and relevance of the study of tumor growth models, a central point of our investigation is the study of the chaotic dynamics and the bifurcation structure of Weibull-Gompertz-Fréchet's functions: a class of continuousdefined one-dimensional maps. Using symbolic dynamics techniques and iteration theory, we established that depending on the properties of this class of functions in a neighborhood of a bifurcation point PBB, in a two-dimensional parameter space, there exists an order regarding how the infinite number of periodic orbits are born: the Sharkovsky ordering. Consequently, the corresponding symbolic sequences follow the usual unimodal kneading sequences in the topological ordered tree. We verified that under some sufficient conditions, Weibull-Gompertz-Fréchet's functions have a particular bifurcation structure: a big bang bifurcation point PBB. This fractal bifurcations structure is of the so-called "box-within-a-box" type, associated to a boxe ω1, where an infinite number of bifurcation curves issues from. This analysis is done making use of fold and flip bifurcation curves and symbolic dynamics techniques. The present paper is an original contribution in the framework of the big bang bifurcation analysis for continuous maps.

On the numerical computation of the Mittag-Leffler function

Recently simple limiting functions establishing upper and lower bounds on the Mittag-Leffler function were found. This paper follows those expressions to design an efficient algorithm for the approximate calculation of expressions usual in fractional-order control systems. The numerical experiments demonstrate the superior efficiency of the proposed method.

Spatial neighborhood matrix computation: Inverse distance weighted versus binary contiguity

Paper presented at Geo-Spatial Crossroad GI_Forum, Salzburg, Austria.

A logical foundation for session-based concurrent computation

Linear logic has long been heralded for its potential of providing a logical basis for concurrency. While over the years many research attempts were made in this regard, a Curry-Howard correspondence between linear logic and concurrent computation was only found recently, bridging the proof theory of linear logic and session-typed process calculus. Building upon this work, we have developed a theory of intuitionistic linear logic as a logical foundation for session-based concurrent computation, exploring several concurrency related phenomena such as value-dependent session types and polymorphic sessions within our logical framework in an arguably clean and elegant way, establishing with relative ease strong typing guarantees due to the logical basis, which ensure the fundamental properties of type preservation and global progress, entailing the absence of deadlocks in communication. We develop a general purpose concurrent programming language based on the logical interpretation, combining functional programming with a concurrent, session-based process layer through the form of a contextual monad, preserving our strong typing guarantees of type preservation and deadlock-freedom in the presence of general recursion and higher-order process communication. We introduce a notion of linear logical relations for session typed concurrent processes, developing an arguably uniform technique for reasoning about sophisticated properties of session-based concurrent computation such as termination or equivalence based on our logical approach, further supporting our goal of establishing intuitionistic linear logic as a logical foundation for sessionbased concurrency.

Minimal computation structures for visual information applications based on printed electronics

In the early nineties, Mark Weiser wrote a series of seminal papers that introduced the concept of Ubiquitous Computing. According to Weiser, computers require too much attention from the user, drawing his focus from the tasks at hand. Instead of being the centre of attention, computers should be so natural that they would vanish into the human environment. Computers become not only truly pervasive but also effectively invisible and unobtrusive to the user. This requires not only for smaller, cheaper and low power consumption computers, but also for equally convenient display solutions that can be harmoniously integrated into our surroundings. With the advent of Printed Electronics, new ways to link the physical and the digital worlds became available. By combining common printing techniques such as inkjet printing with electro-optical functional inks, it is starting to be possible not only to mass-produce extremely thin, flexible and cost effective electronic circuits but also to introduce electronic functionalities into products where it was previously unavailable. Indeed, Printed Electronics is enabling the creation of novel sensing and display elements for interactive devices, free of form factor. At the same time, the rise in the availability and affordability of digital fabrication technologies, namely of 3D printers, to the average consumer is fostering a new industrial (digital) revolution and the democratisation of innovation. Nowadays, end-users are already able to custom design and manufacture on demand their own physical products, according to their own needs. In the future, they will be able to fabricate interactive digital devices with user-specific form and functionality from the comfort of their homes. This thesis explores how task-specific, low computation, interactive devices capable of presenting dynamic visual information can be created using Printed Electronics technologies, whilst following an approach based on the ideals behind Personal Fabrication. Focus is given on the use of printed electrochromic displays as a medium for delivering dynamic digital information. According to the architecture of the displays, several approaches are highlighted and categorised. Furthermore, a pictorial computation model based on extended cellular automata principles is used to programme dynamic simulation models into matrix-based electrochromic displays. Envisaged applications include the modelling of physical, chemical, biological, and environmental phenomena.

Ontology-based representation and generation of workflows for micro-task human-machine computation

Doctoral Program in Computer Science

Combining data mining and evolutionary computation for multi-criteria optimization of earthworks

Earthworks tasks aim at levelling the ground surface at a target construction area and precede any kind of structural construction (e.g., road and railway construction). It is comprised of sequential tasks, such as excavation, transportation, spreading and compaction, and it is strongly based on heavy mechanical equipment and repetitive processes. Under this context, it is essential to optimize the usage of all available resources under two key criteria: the costs and duration of earthwork projects. In this paper, we present an integrated system that uses two artificial intelligence based techniques: data mining and evolutionary multi-objective optimization. The former is used to build data-driven models capable of providing realistic estimates of resource productivity, while the latter is used to optimize resource allocation considering the two main earthwork objectives (duration and cost). Experiments held using real-world data, from a construction site, have shown that the proposed system is competitive when compared with current manual earthwork design.