The massless two-loop two-point function and zeta functions in counterterms of Feynman diagrams

The main part of this thesis describes a method of calculating the massless two-loop two-point function which allows expanding the integral up to an arbitrary order in the dimensional regularization parameter epsilon by rewriting it as a double Mellin-Barnes integral. Closing the contour and collecting the residues then transforms this integral into a form that enables us to utilize S. Weinzierl's computer library nestedsums. We could show that multiple zeta values and rational numbers are sufficient for expanding the massless two-loop two-point function to all orders in epsilon. We then use the Hopf algebra of Feynman diagrams and its antipode, to investigate the appearance of Riemann's zeta function in counterterms of Feynman diagrams in massless Yukawa theory and massless QED. The class of Feynman diagrams we consider consists of graphs built from primitive one-loop diagrams and the non-planar vertex correction, where the vertex corrections only depend on one external momentum. We showed the absence of powers of pi in the counterterms of the non-planar vertex correction and diagrams built by shuffling it with the one-loop vertex correction. We also found the invariance of some coefficients of zeta functions under a change of momentum flow through these vertex corrections.

(Figures S2a-c) Phase diagrams of the upper crust, the lower crust and the upper mantle based on averaged compositions of the oceanic crust and mantle

The age of the subducting Nazca Plate off Chile increases northwards from 0 Ma at the Chile Triple Junction (46°S) to 37 Ma at the latitude of Valparaíso (32°S). Age-related variations in the thermal state of the subducting plate impact on (a) the water influx to the subduction zone, as well as on (b) the volumes of water that are released under the continental forearc or, alternatively, carried beyond the arc. Southern Central Chile is an ideal setting to study this effect, because other factors for the subduction zone water budget appear constant. We determine the water influx by calculating the crustal water uptake and by modeling the upper mantle serpentinization at the outer rise of the Chile Trench. The water release under forearc and arc is determined by coupling FEM thermal models of the subducting plate with stability fields of water-releasing mineral reactions for upper and lower crust and hydrated mantle. Results show that both the influx of water stored in, and the outflux of water released from upper crust, lower crust and mantle vary drastically over segment boundaries. In particular, the oldest and coldest segments carry roughly twice as much water into the subduction zone as the youngest and hottest segments, but their release flux to the forearc is only about one fourth of the latter. This high variability over a subduction zone of < 1500 km length shows that it is insufficient to consider subduction zones as uniform entities in global estimates of subduction zone fluxes. This article is protected by copyright. All rights reserved.

Information integration: from P&I diagrams to functional models

Information integration is a very important topic. Reusing the knowledge and having common and exchangeable representations have been an active research topic in process systems engineering. In this paper we deal with information integration in two different ways, the first one sharing knowledge between different heterogeneous applications and the second one integrating two different (but complementary) types of knowledge: functional and structural. A new architecture to integrate these representation and use for several purposes is presented in this paper.

Analysis of neuronal functions based on feynman diagrams

A method to study some neuronal functions, based on the use of the Feynman diagrams, employed in many-body theory, is reported. An equation obtained from the neuron cable theory is the basis for the method. The Green's function for this equation is obtained under some simple boundary conditions. An excitatory signal, with different conditions concerning high and pulse duration, is employed as input signal. Different responses have been obtained

Zone design of specific sizes using adaptive additively weighted voronoi diagrams

Territory or zone design processes entail partitioning a geographic space, organized as a set of areal units, into different regions or zones according to a specific set of criteria that are dependent on the application context. In most cases, the aim is to create zones of approximately equal sizes (zones with equal numbers of inhabitants, same average sales, etc.). However, some of the new applications that have emerged, particularly in the context of sustainable development policies, are aimed at defining zones of a predetermined, though not necessarily similar, size. In addition, the zones should be built around a given set of seeds. This type of partitioning has not been sufficiently researched; therefore, there are no known approaches for automated zone delimitation. This study proposes a new method based on a discrete version of the adaptive additively weighted Voronoi diagram that makes it possible to partition a two-dimensional space into zones of specific sizes, taking both the position and the weight of each seed into account. The method consists of repeatedly solving a traditional additively weighted Voronoi diagram, so that each seed?s weight is updated at every iteration. The zones are geographically connected using a metric based on the shortest path. Tests conducted on the extensive farming system of three municipalities in Castile-La Mancha (Spain) have established that the proposed heuristic procedure is valid for solving this type of partitioning problem. Nevertheless, these tests confirmed that the given seed position determines the spatial configuration the method must solve and this may have a great impact on the resulting partition.

Use of Feynman diagrams in large-scale neural networks with nonlinear behaviour

A new proposal to the study of large-scale neural networks is reported. It is based on the use of similar graphs to the Feynman diagrams. A first general theory is presented and some interpretations are given. A propagator, based on the Green's function of the neuron, is the basis of the method. Application to a simple case is reported.

Analysis of large-scale digital optical neural networks by Feynman diagrams

A new method to study large scale neural networks is presented in this paper. The basis is the use of Feynman- like diagrams. These diagrams allow the analysis of collective and cooperative phenomena with a similar methodology to the employed in the Many Body Problem. The proposed method is applied to a very simple structure composed by an string of neurons with interaction among them. It is shown that a new behavior appears at the end of the row. This behavior is different to the initial dynamics of a single cell. When a feedback is present, as in the case of the hippocampus, this situation becomes more complex with a whole set of new frequencies, different from the proper frequencies of the individual neurons. Application to an optical neural network is reported.