The Surface Laplacian Technique in EEG: Theory and Methods

This paper reviews the method of surface Laplacian differentiation to study EEG. We focus on topics that are helpful for a clear understanding of the underlying concepts and its efficient implementation, which is especially important for EEG researchers unfamiliar with the technique. The popular methods of finite difference and splines are reviewed in detail. The former has the advantage of simplicity and low computational cost, but its estimates are prone to a variety of errors due to discretization. The latter eliminates all issues related to discretization and incorporates a regularization mechanism to reduce spatial noise, but at the cost of increasing mathematical and computational complexity. These and several others issues deserving further development are highlighted, some of which we address to the extent possible. Here we develop a set of discrete approximations for Laplacian estimates at peripheral electrodes and a possible solution to the problem of multiple-frame regularization. We also provide the mathematical details of finite difference approximations that are missing in the literature, and discuss the problem of computational performance, which is particularly important in the context of EEG splines where data sets can be very large. Along this line, the matrix representation of the surface Laplacian operator is carefully discussed and some figures are given illustrating the advantages of this approach. In the final remarks, we briefly sketch a possible way to incorporate finite-size electrodes into Laplacian estimates that could guide further developments.Comment: 43 pages, 8 figure

Mission and worship in the age of the Spirit

Using Paul Tillich's method of the correlation, this article relates the relations between the inside and the outside of the worship space, relating worship and mission. At the end, the fourfold of the worship is re-interpreted.Using Paul Tillich's method of the correlation, this article relates the relations between the inside and the outside of the worship space, relating worship and mission. At the end, the fourfold of the worship is re-interpreted. 

Eucharist/ Communion/ Lord’s Supper – The utopia of Jesus in our days

The Lord's Supper/Communion/Eucharist is one of the most powerful rituals of the Christian faith. In this chapter, I try to expand the understanding of this precious meal for our time. In order to do that I introduce the meal as an overarching event in the life of the world and consider some communitarian, social conditions, as strong characteristics of this meal. With that information, I go through the New Testament to see what was happening at the beginning of the church. After that I develop some fundamental aspects of the Eucharistic meal for our time considering the possible relations between Eucharist and Socialism, associating this Christian ritual with social visibility and against social humiliation. I finish mentioning Clarice Lispector a Brazilian writer who said that "love is bread shared among strangers." The Lord's Supper/Communion/Eucharist is one of the most powerful rituals of the Christian faith. In this chapter, I try to expand the understanding of this precious meal for our time. In order to do that I introduce the meal as an overarching event in the life of the world and consider some communitarian, social conditions, as strong characteristics of this meal. With that information, I go through the New Testament to see what was happening at the beginning of the church. After that I develop some fundamental aspects of the Eucharistic meal for our time considering the possible relations between Eucharist and Socialism, associating this Christian ritual with social visibility and against social humiliation. I finish mentioning Clarice Lispector a Brazilian writer who said that "love is bread shared among strangers."

APPROACH OF THE SYSTEMIC DESIGN IN MATERIAL AND INTANGIBLE CULTURE OF ESTRADA REAL: TERRITORIAL SERRO CASE

This study aimed to apply the Systemic Design methodology in the context of the Estrada Real (Royal Road), specifically in Serro Territory, in order to generate a new economic and development model in this location, by creating relationships between their production systems. The first step of the methodology involved the understanding the territory in all its amplitude, i.e., the history of the place, its physical and climatic aspects, its natural resources, its activities (social, cultural and productive), the way and the pace of life community, as well as its infrastructure. The second phase encompassed the systematization and analysis of existing artisanal production systems in Serro Territory. For such a field survey was conducted in which the artisans were interviewed and the production sites were visited. On this occasion, we investigated all output and input of their activities. In the third step of the methodology were designed the matter and energy flows of the nine production systems in question, from the analysis of the "negative points" that emerged in the previous step, as well as the characteristics and potential of the material and immaterial local resources. This process allowed the emergence of several new activities and new products. In the fourth and last step, the current system (existing) and the systemic system (proposed) were compared. Such confrontation demonstrated that, with the approach of Systemic Design the same territory would come to get, on average, an increase of 530% of products and 820% of activity, resulting therefore in a huge business volume. As envisioned results are highlighted: i) in the economic field: expansion of activities; increase in jobs; increase income generation in the community; ii) in the environmental sphere: sustainable management of natural resources; iii) in the cultural field: appreciation of culture; enhancement of local know-how; iv) in the social sector: improving quality of life; keeps its inhabitants in their territory

The Thirring interaction in the two-dimensional axial-current-pseudoscalar derivative coupling model

The authors reexamine the two-dimensional model of massive fermions interacting with a massless pseudoscalar field via axial-current-pseudoscalar derivative coupling. Performing a canonical field transformation on the Bose field algebra the model is mapped into the Thirring model with an additional vector-current-scalar-derivative interaction (Schroer-Thirring model). The complete bosonized version of the model is presented. The bosonized composite operators of the quantum Hamiltonian are obtained as the leading operators in the Wilson short distance expansion.Comment: 13 page