System Modeling and Control Through Fractional-Order Algorithms

The theory of fractional calculus goes back to the beginning of thr throry of differential calculus but its inherent complexity postponed the applications of the associated concepts. In the last decade the progress in the areas of chaos and fractals revealed subtle relationships with the fractional calculus leading to an increasing interest in the development of the new paradigm. In the area of automaticcontrol preliminary work has already been carried out but the proposed algorithms are restricted to the frequency domain. The paper discusses the design of fractional-order discrete-time controllers. The algorithms studied adopt the time domein, which makes them suited for z-transform analusis and discrete-time implementation. The performance of discrete-time fractional-order controllers with linear and non-linear systems is also investigated.

On local fractional continuous wavelet transform

We introduce a new wavelet transform within the framework of the local fractional calculus. An illustrative example of local fractional wavelet transform is also presented.

Regulation of histone H2A.Z expression is mediated by sirtuin 1 in prostate cancer

Histone variants seem to play a major role in gene expression regulation. In prostate cancer, H2A.Z and its acetylated form are implicated in oncogenes’ upregulation. SIRT1, which may act either as tumor suppressor or oncogene, reduces H2A.Z levels in cardiomyocytes, via proteasome-mediated degradation, and this mechanism might be impaired in prostate cancer cells due to sirtuin 1 downregulation. Thus, we aimed to characterize the mechanisms underlying H2A.Z and SIRT1 deregulation in prostate carcinogenesis and how they interact. We found that H2AFZ and SIRT1 were up- and downregulated, respectively, at transcript level in primary prostate cancer and high-grade prostatic intraepithelial neoplasia compared to normal prostatic tissues. Induced SIRT1 overexpression in prostate cancer cell lines resulted in almost complete absence of H2A.Z. Inhibition of mTOR had a modest effect on H2A.Z levels, but proteasome inhibition prevented the marked reduction of H2A.Z due to sirtuin 1 overexpression. Prostate cancer cells exposed to epigenetic modifying drugs trichostatin A, alone or combined with 5-aza-2’-deoxycytidine, increased H2AFZ transcript, although with a concomitant decrease in protein levels. Conversely, SIRT1 transcript and protein levels increased after exposure. ChIP revealed an increase of activation marks within the TSS region for both genes. Remarkably, inhibition of sirtuin 1 with nicotinamide, increased H2A.Z levels, whereas activation of sirtuin 1 by resveratrol led to an abrupt decrease in H2A.Z. Finally, protein-ligation assay showed that exposure to epigenetic modifying drugs fostered the interaction between sirtuin 1 and H2A.Z. We concluded that sirtuin 1 and H2A.Z deregulation in prostate cancer are reciprocally related. Epigenetic mechanisms, mostly histone post-translational modifications, are likely involved and impair sirtuin 1-mediated downregulation of H2A.Z via proteasome-mediated degradation. Epigenetic modifying drugs in conjunction with enzymatic modulators are able to restore the normal functions of sirtuin 1 and might constitute relevant tools for targeted therapy of prostate cancer patients

Application of continuous wavelet transform to the analysis of the modulus of the fractional Fourier transform bands for resolving two component mixture

In this paper, the fractional Fourier transform (FrFT) is applied to the spectral bands of two component mixture containing oxfendazole and oxyclozanide to provide the multicomponent quantitative prediction of the related substances. With this aim in mind, the modulus of FrFT spectral bands are processed by the continuous Mexican Hat family of wavelets, being denoted by MEXH-CWT-MOFrFT. Four modulus sets are obtained for the parameter a of the FrFT going from 0.6 up to 0.9 in order to compare their effects upon the spectral and quantitative resolutions. Four linear regression plots for each substance were obtained by measuring the MEXH-CWT-MOFrFT amplitudes in the application of the MEXH family to the modulus of the FrFT. This new combined powerful tool is validated by analyzing the artificial samples of the related drugs, and it is applied to the quality control of the commercial veterinary samples.

Analysis of financial indices by means of the windowed Fourier transform

The goal of this study is to analyze the dynamical properties of financial data series from nineteen worldwide stock market indices (SMI) during the period 1995–2009. SMI reveal a complex behavior that can be explored since it is available a considerable volume of data. In this paper is applied the window Fourier transform and methods of fractional calculus. The results reveal classification patterns typical of fractional order systems.

Analysis of financial data series using fractional Fourier transform and multidimensional scaling

The goal of this study is the analysis of the dynamical properties of financial data series from worldwide stock market indexes during the period 2000–2009. We analyze, under a regional criterium, ten main indexes at a daily time horizon. The methods and algorithms that have been explored for the description of dynamical phenomena become an effective background in the analysis of economical data. We start by applying the classical concepts of signal analysis, fractional Fourier transform, and methods of fractional calculus. In a second phase we adopt the multidimensional scaling approach. Stock market indexes are examples of complex interacting systems for which a huge amount of data exists. Therefore, these indexes, viewed from a different perspectives, lead to new classification patterns.

Dynamics of the Dow Jones and the NASDAQ stock indexes

The goal of this study is the analysis of the dynamical properties of financial data series from worldwide stock market indices. We analyze the Dow Jones Industrial Average ( ∧ DJI) and the NASDAQ Composite ( ∧ IXIC) indexes at a daily time horizon. The methods and algorithms that have been explored for description of physical phenomena become an effective background, and even inspiration, for very productive methods used in the analysis of economical data. We start by applying the classical concepts of signal analysis, Fourier transform, and methods of fractional calculus. In a second phase we adopt a pseudo phase plane approach.

Robotic manipulators with vibrations: short time fourier transform of fractional spectra

This paper analyzes the signals captured during impacts and vibrations of a mechanical manipulator. In order to acquire and study the signals an experimental setup is implemented. The signals are treated through signal processing tools such as the fast Fourier transform and the short time Fourier transform. The results show that the Fourier spectrum of several signals presents a non integer behavior. The experimental study provides valuable results that can assist in the design of a control system to deal with the unwanted effects of vibrations.

Simulation and dynamics of freeway traffic

This paper presents the new package entitled Simulator of Intelligent Transportation Systems (SITS) and a computational oriented analysis of traffic dynamics. The SITS adopts a microscopic simulation approach to reproduce real traffic conditions considering different types of vehicles, drivers and roads. A set of experiments with the SITS reveal the dynamic phenomena exhibited by this kind of system. For this purpose a modelling formalism is developed that embeds the statistics and the Laplace transform. The results make possible the adoption of classical system theory tools and point out that it is possible to study traffic systems taking advantage of the knowledge gathered with automatic control algorithms. A complementary perspective for the analysis of the traffic flow is also quantified through the entropy measure.

An integer programming framework for sequencing cutting patterns based on interval graph completion

We derived a framework in integer programming, based on the properties of a linear ordering of the vertices in interval graphs, that acts as an edge completion model for obtaining interval graphs. This model can be applied to problems of sequencing cutting patterns, namely the minimization of open stacks problem (MOSP). By making small modifications in the objective function and using only some of the inequalities, the MOSP model is applied to another pattern sequencing problem that aims to minimize, not only the number of stacks, but also the order spread (the minimization of the stack occupation problem), and the model is tested.

An integer programming model for the minimum interval graph completion problem

The minimum interval graph completion problem consists of, given a graph G = ( V, E ), finding a supergraph H = ( V, E ∪ F ) that is an interval graph, while adding the least number of edges |F| . We present an integer programming formulation for solving the minimum interval graph completion problem recurring to a characteri- zation of interval graphs that produces a linear ordering of the maximal cliques of the solution graph.

Minimization of open orders using interval graphs

In this paper we address an order processing optimization problem known as the Minimization of Open Stacks Problem (MOSP). This problem consists in finding the best sequence for manufacturing the different products required by costumers, in a setting where only one product can be made at a time. The objective is to minimize the maximum number of incomplete orders from costumers that are being processed simultaneously. We present an integer programming model, based on the existence of a perfect elimination order in interval graphs, which finds an optimal sequence for the costumers orders. Among other economic advantages, manufacturing the products in this optimal sequence reduces the amount of space needed to store incomplete orders.

Sequencing cutting patterns with colored interval graphs

The problem addressed here originates in the industry of flat glass cutting and wood panel sawing, where smaller items are cut from larger items accordingly to predefined cutting patterns. In this type of industry the smaller pieces that are cut from the patterns are piled around the machine in stacks according to the size of the pieces, which are moved to the warehouse only when all items of the same size have been cut. If the cutting machine can process only one pattern at a time, and the workspace is limited, it is desirable to set the sequence in which the cutting patterns are processed in a way to minimize the maximum number of open stacks around the machine. This problem is known in literature as the minimization of open stacks (MOSP). To find the best sequence of the cutting patterns, we propose an integer programming model, based on interval graphs, that searches for an appropriate edge completion of the given graph of the problem, while defining a suitable coloring of its vertices.

Using interval graphs in an order processing optimization problem

In this paper we address an order processing optimization problem known as minimization of open stacks (MOSP). We present an integer pro gramming model, based on the existence of a perfect elimination scheme in interval graphs, which finds an optimal sequence for the costumers orders.

Data Extraction Tool to Analyse, Transform and Store Real Data from Electricity Markets

The study of electricity markets operation has been gaining an increasing importance in the last years, as result of the new challenges that the restructuring process produced. Currently, lots of information concerning electricity markets is available, as market operators provide, after a period of confidentiality, data regarding market proposals and transactions. These data can be used as source of knowledge to define realistic scenarios, which are essential for understanding and forecast electricity markets behavior. The development of tools able to extract, transform, store and dynamically update data, is of great importance to go a step further into the comprehension of electricity markets and of the behaviour of the involved entities. In this paper an adaptable tool capable of downloading, parsing and storing data from market operators’ websites is presented, assuring constant updating and reliability of the stored data.