Clifford-Hermite polynomials in fractional Clifford analysis

In this paper we generalize radial and standard Clifford-Hermite polynomials to the new framework of fractional Clifford analysis with respect to the Riemann-Liouville derivative in a symbolic way. As main consequence of this approach, one does not require an a priori integration theory. Basic properties such as orthogonality relations, differential equations, and recursion formulas, are proven.

Orthogonal persistence in Java supported by aspect- oriented programming and reflection

The persistence concern implemented as an aspect has been studied since the appearance of the Aspect-Oriented paradigm. Frequently, persistence is given as an example that can be aspectized, but until today no real world solution has applied that paradigm. Such solution should be able to enhance the programmer productivity and make the application less prone to errors. To test the viability of that concept, in a previous study we developed a prototype that implements Orthogonal Persistence as an aspect. This first version of the prototype was already fully functional with all Java types including arrays. In this work the results of our new research to overcome some limitations that we have identified on the data type abstraction and transparency in the prototype are presented. One of our goals was to avoid the Java standard idiom for genericity, based on casts, type tests and subtyping. Moreover, we also find the need to introduce some dynamic data type abilities. We consider that the Reflection is the solution to those issues. To achieve that, we have extended our prototype with a new static weaver that preprocesses the application source code in order to introduce changes to the normal behavior of the Java compiler with a new generated reflective code.

An aspect-oriented framework for orthogonal persistence

The life cycle of software applications in general is very short and with extreme volatile requirements. Within these conditions programmers need development tools and techniques with an extreme level of productivity. We consider the code reuse as the most prominent approach to solve that problem. Our proposal uses the advantages provided by the Aspect-Oriented Programming in order to build a reusable framework capable to turn both programmer and application oblivious as far as data persistence is concerned, thus avoiding the need to write any line of code about that concern. Besides the benefits to productivity, the software quality increases. This paper describes the actual state of the art, identifying the main challenge to build a complete and reusable framework for Orthogonal Persistence in concurrent environments with support for transactions. The present work also includes a successfully developed prototype of that framework, capable of freeing the programmer of implementing any read or write data operations. This prototype is supported by an object oriented database and, in the future, will also use a relational database and have support for transactions.

Fast and efficient user pairing and power allocation algorithm for non-orthogonal multiple access in cellular networks

Non-orthogonal multiple access (NOMA) is emerging as a promising multiple access technology for the fifth generation cellular networks to address the fast growing mobile data traffic. It applies superposition coding in transmitters, allowing simultaneous allocation of the same frequency resource to multiple intra-cell users. Successive interference cancellation is used at the receivers to cancel intra-cell interference. User pairing and power allocation (UPPA) is a key design aspect of NOMA. Existing UPPA algorithms are mainly based on exhaustive search method with extensive computation complexity, which can severely affect the NOMA performance. A fast proportional fairness (PF) scheduling based UPPA algorithm is proposed to address the problem. The novel idea is to form user pairs around the users with the highest PF metrics with pre-configured fixed power allocation. Systemlevel simulation results show that the proposed algorithm is significantly faster (seven times faster for the scenario with 20 users) with a negligible throughput loss than the existing exhaustive search algorithm.

Euclidean Distance Between Haar Orthogonal and Gaussian Matrices

In this work, we study a version of the general question of how well a Haar-distributed orthogonal matrix can be approximated by a random Gaussian matrix. Here, we consider a Gaussian random matrix (Formula presented.) of order n and apply to it the Gram–Schmidt orthonormalization procedure by columns to obtain a Haar-distributed orthogonal matrix (Formula presented.). If (Formula presented.) denotes the vector formed by the first m-coordinates of the ith row of (Formula presented.) and (Formula presented.), our main result shows that the Euclidean norm of (Formula presented.) converges exponentially fast to (Formula presented.), up to negligible terms. To show the extent of this result, we use it to study the convergence of the supremum norm (Formula presented.) and we find a coupling that improves by a factor (Formula presented.) the recently proved best known upper bound on (Formula presented.). Our main result also has applications in Quantum Information Theory.

On polynomials with given Hilbert function and applications

Using Macaulay's correspondence we study the family of Artinian Gorenstein local algebras with fixed symmetric Hilbert function decomposition. As an application we give a new lower bound for the dimension of cactus varieties of the third Veronese embedding. We discuss the case of cubic surfaces, where interesting phenomena occur.

Synthesis of thioenol ether functionalized cyclooctyne and its orthogonal cycloaddition sequence

In this work, the synthesis of a new bifunctionalized cyclooctyne for a possible layer by layer surface functionalization is presented. The main objective is to find a more stable molecule than the literature known methyl enol ether substituted cyclooctyne. Accordingly, the two target functionalities are an internal alkyne group and a vinyl methyl sulfide group. The synthesis was achieved in 9 steps and consists first of all in the preparation of an aldehyde starting from 1,5-cyclooctadiene with a cyclopropanation reaction followed by a reduction and the SWERN oxidation to an aldehyde. The new functionality was introduced by exploiting the WITTIG reaction. For the alkyne group a bromination followed by a double elimination gave good results. The reactivity of the new molecule was tested using a sequential application of SPAAC and iEDDA reactions, comparing it with the cyclooctyne functionalized with a methyl enol ether. Concerning the comparison of both compounds the sulfur ether is significantly slower and therefore more stable. It will be tested in the future for surface functionalization from the KOERT group.

Orthogonal chirp division multiplexing: performance evaluation in the presence of phase noise

In Beyond 5G technologies, Terahertz communications will be used: frequency bands between 100 GHz and 10 THz will be exploited in order to have higher throughput and lower latency. Those frequency bands suffer from several impairments, and it is thought that phase noise is one of the most significant. Orthogonal Chirp Division Multiplexing (OCDM) might be used in Beyond 5G communications, thanks to its robustness to multipath fading: it outperforms Orthogonal Frequency Division Multiplexing (OFDM) systems. The aim of this thesis is to find a suitable model for describing phase noise in Terahertz communications, and to study the performance of an OCDM system affected by this impairment. After this, a simple compensation scheme is introduced, and the improvement that it provides is analysed. The thesis is organized as follow: in the first chapter Terahertz communications and Beyond 5G are introduced, in the second chapter phase noise is studied, in the third chapter OCDM is analysed, and in the fourth chapter numerical results are presented.

Decompositions of powers of quadratic forms

We analyze the Waring decompositions of the powers of any quadratic form over the field of complex numbers. Our main objective is to provide detailed information about their rank and border rank. These forms are of significant importance because of the classical decomposition expressing the space of polynomials of a fixed degree as a direct sum of the spaces of harmonic polynomials multiplied by a power of the quadratic form. Using the fact that the spaces of harmonic polynomials are irreducible representations of the special orthogonal group over the field of complex numbers, we show that the apolar ideal of the s-th power of a non-degenerate quadratic form in n variables is generated by the set of harmonic polynomials of degree s+1. We also generalize and improve upon some of the results about real decompositions, provided by B. Reznick in his notes from 1992, focusing on possibly minimal decompositions and providing new ones, both real and complex. We investigate the rank of the second power of a non-degenerate quadratic form in n variables, which is equal to (n^2+n+2)/2 in most cases. We also study the border rank of any power of an arbitrary ternary non-degenerate quadratic form, which we determine explicitly using techniques of apolarity and a specific subscheme contained in its apolar ideal. Based on results about smoothability, we prove that the smoothable rank of the s-th power of such form corresponds exactly to its border rank and to the rank of its middle catalecticant matrix, which is equal to (s+1)(s+2)/2.

A novel approach to Non-Orthogonal Random Access with application to NB-IoT NTN systems

In the Massive IoT vision, millions of devices need to be connected to the Internet through a wireless access technology. However, current IoT-focused standards are not fully prepared for this future. In this thesis, a novel approach to Non-Orthogonal techniques for Random Access, which is the main bottleneck in high density systems, is proposed. First, the most popular wireless access standards are presented, with a focus on Narrowband-IoT. Then, the Random Access procedure as implemented in NB-IoT is analyzed. The Non-Orthogonal Random Access technique is presented next, along with two potential algorithms for the detection of non-orthogonal preambles. Finally, the performance of the proposed solutions are obtained through numerical simulations.

Neural Network based Non Orthogonal Random Access for 6G NTN-IoT

Pervasive and distributed Internet of Things (IoT) devices demand ubiquitous coverage beyond No-man’s land. To satisfy plethora of IoT devices with resilient connectivity, Non-Terrestrial Networks (NTN) will be pivotal to assist and complement terrestrial systems. In a massiveMTC scenario over NTN, characterized by sporadic uplink data reports, all the terminals within a satellite beam shall be served during the short visibility window of the flying platform, thus generating congestion due to simultaneous access attempts of IoT devices on the same radio resource. The more terminals collide, the more average-time it takes to complete an access which is due to the decreased number of successful attempts caused by Back-off commands of legacy methods. A possible countermeasure is represented by Non-Orthogonal Multiple Access scheme, which requires the knowledge of the number of superimposed NPRACH preambles. This work addresses this problem by proposing a Neural Network (NN) algorithm to cope with the uncoordinated random access performed by a prodigious number of Narrowband-IoT devices. Our proposed method classifies the number of colliding users, and for each estimates the Time of Arrival (ToA). The performance assessment, under Line of Sight (LoS) and Non-LoS conditions in sub-urban environments with two different satellite configurations, shows significant benefits of the proposed NN algorithm with respect to traditional methods for the ToA estimation.

Transmission Of Intra-cellular Genetic Information: A System Proposal.

One of the great challenges of the scientific community on theories of genetic information, genetic communication and genetic coding is to determine a mathematical structure related to DNA sequences. In this paper we propose a model of an intra-cellular transmission system of genetic information similar to a model of a power and bandwidth efficient digital communication system in order to identify a mathematical structure in DNA sequences where such sequences are biologically relevant. The model of a transmission system of genetic information is concerned with the identification, reproduction and mathematical classification of the nucleotide sequence of single stranded DNA by the genetic encoder. Hence, a genetic encoder is devised where labelings and cyclic codes are established. The establishment of the algebraic structure of the corresponding codes alphabets, mappings, labelings, primitive polynomials (p(x)) and code generator polynomials (g(x)) are quite important in characterizing error-correcting codes subclasses of G-linear codes. These latter codes are useful for the identification, reproduction and mathematical classification of DNA sequences. The characterization of this model may contribute to the development of a methodology that can be applied in mutational analysis and polymorphisms, production of new drugs and genetic improvement, among other things, resulting in the reduction of time and laboratory costs.

Study Of The Homogeneity Of Drug Loaded In Polymeric Films Using Near-infrared Chemical Imaging And Split-plot Design.

Split-plot design (SPD) and near-infrared chemical imaging were used to study the homogeneity of the drug paracetamol loaded in films and prepared from mixtures of the biocompatible polymers hydroxypropyl methylcellulose, polyvinylpyrrolidone, and polyethyleneglycol. The study was split into two parts: a partial least-squares (PLS) model was developed for a pixel-to-pixel quantification of the drug loaded into films. Afterwards, a SPD was developed to study the influence of the polymeric composition of films and the two process conditions related to their preparation (percentage of the drug in the formulations and curing temperature) on the homogeneity of the drug dispersed in the polymeric matrix. Chemical images of each formulation of the SPD were obtained by pixel-to-pixel predictions of the drug using the PLS model of the first part, and macropixel analyses were performed for each image to obtain the y-responses (homogeneity parameter). The design was modeled using PLS regression, allowing only the most relevant factors to remain in the final model. The interpretation of the SPD was enhanced by utilizing the orthogonal PLS algorithm, where the y-orthogonal variations in the design were separated from the y-correlated variation.

Estilos motivacionais de professores: propriedades psicométricas de um instrumento de avaliação

The purpose of this study was to conduct an exploratory factorial analysis of Problems in School, a teachers' motivational styles evaluation instrument, constructed by Deci et al. The original instrument is in a Likert-scale format with the underlying assumption of the existence of a continuum of four different styles contributing to promote students' autonomy. Translated into portuguese, the instrument was applied to 582 elementary and junior high school teachers from several regions of Brazil. Factorial analyses revealed a solution with four orthogonal distinct factors, the authors' initial supposition (existence of a continuum) was not confirmed. In fact, only two opposite styles (both high promotion of autonomy and of control) corresponded to the Deci et al. original ideas. Problems regarding the validity of the other remaining styles emerged. Data was discussed and a revised version of the scale was developed. Directions for further research were also suggested.