Rational algorithms for the decomposition of Feynman integrals via intersection theory

The decomposition of Feynman integrals into a basis of independent master integrals is an essential ingredient of high-precision theoretical predictions, that often represents a major bottleneck when processes with a high number of loops and legs are involved. In this thesis we present a new algorithm for the decomposition of Feynman integrals into master integrals with the formalism of intersection theory. Intersection theory is a novel approach that allows to decompose Feynman integrals into master integrals via projections, based on a scalar product between Feynman integrals called intersection number. We propose a new purely rational algorithm for the calculation of intersection numbers of differential $n-$forms that avoids the presence of algebraic extensions. We show how expansions around non-rational poles, which are a bottleneck of existing algorithms for intersection numbers, can be avoided by performing an expansion in series around a rational polynomial irreducible over $\mathbb{Q}$, that we refer to as $p(z)-$adic expansion. The algorithm we developed has been implemented and tested on several diagrams, both at one and two loops.

Characterisation of anatomical properties of the human basal ganglia using magnetic resonance imaging

The detailed in-vivo characterization of subcortical brain structures is essential not only to understand the basic organizational principles of the healthy brain but also for the study of the involvement of the basal ganglia in brain disorders. The particular tissue properties of basal ganglia - most importantly their high iron content, strongly affect the contrast of magnetic resonance imaging (MRI) images, hampering the accurate automated assessment of these regions. This technical challenge explains the substantial controversy in the literature about the magnitude, directionality and neurobiological interpretation of basal ganglia structural changes estimated from MRI and computational anatomy techniques. My scientific project addresses the pertinent need for accurate automated delineation of basal ganglia using two complementary strategies: ? Empirical testing of the utility of novel imaging protocols to provide superior contrast in the basal ganglia and to quantify brain tissue properties; ? Improvement of the algorithms for the reliable automated detection of basal ganglia and thalamus Previous research demonstrated that MRI protocols based on magnetization transfer (MT) saturation maps provide optimal grey-white matter contrast in subcortical structures compared with the widely used Tl-weighted (Tlw) images (Helms et al., 2009). Under the assumption of a direct impact of brain tissue properties on MR contrast my first study addressed the question of the mechanisms underlying the regional specificities effect of the basal ganglia. I used established whole-brain voxel-based methods to test for grey matter volume differences between MT and Tlw imaging protocols with an emphasis on subcortical structures. I applied a regression model to explain the observed grey matter differences from the regionally specific impact of brain tissue properties on the MR contrast. The results of my first project prompted further methodological developments to create adequate priors for the basal ganglia and thalamus allowing optimal automated delineation of these structures in a probabilistic tissue classification framework. I established a standardized workflow for manual labelling of the basal ganglia, thalamus and cerebellar dentate to create new tissue probability maps from quantitative MR maps featuring optimal grey-white matter contrast in subcortical areas. The validation step of the new tissue priors included a comparison of the classification performance with the existing probability maps. In my third project I continued investigating the factors impacting automated brain tissue classification that result in interpretational shortcomings when using Tlw MRI data in the framework of computational anatomy. While the intensity in Tlw images is predominantly

The (t) property of some classes of graphs

In this note,the (t) properties of five class are studied. We proved that the classes of cographs and clique perfect graphs without isolated vertices satisfy the (2) property and the (3) property, but do not satisfy the (t) property for tis greater than equal to 4. The (t) properties of the planar graphs and the perfect graphss are also studied . we obtain a necessary and suffieient conditions for the trestled graph of index K to satisfy the (2) property

Median graphs, the remoteness function, periphery transversals, and geodetic number two

A periphery transversal of a median graph G is introduced as a set of vertices that meets all the peripheral subgraphs of G. Using this concept, median graphs with geodetic number 2 are characterized in two ways. They are precisely the median graphs that contain a periphery transversal of order 2 as well as the median graphs for which there exists a profile such that the remoteness function is constant on G. Moreover, an algorithm is presented that decides in O(mlog n) time whether a given graph G with n vertices and m edges is a median graph with geodetic number 2. Several additional structural properties of the remoteness function on hypercubes and median graphs are obtained and some problems listed

On Convergence Properties of the EM Algorithm for Gaussian Mixtures

"Expectation-Maximization'' (EM) algorithm and gradient-based approaches for maximum likelihood learning of finite Gaussian mixtures. We show that the EM step in parameter space is obtained from the gradient via a projection matrix $P$, and we provide an explicit expression for the matrix. We then analyze the convergence of EM in terms of special properties of $P$ and provide new results analyzing the effect that $P$ has on the likelihood surface. Based on these mathematical results, we present a comparative discussion of the advantages and disadvantages of EM and other algorithms for the learning of Gaussian mixture models.

Dynamic load balancing for the distributed mining of molecular structures

In molecular biology, it is often desirable to find common properties in large numbers of drug candidates. One family of methods stems from the data mining community, where algorithms to find frequent graphs have received increasing attention over the past years. However, the computational complexity of the underlying problem and the large amount of data to be explored essentially render sequential algorithms useless. In this paper, we present a distributed approach to the frequent subgraph mining problem to discover interesting patterns in molecular compounds. This problem is characterized by a highly irregular search tree, whereby no reliable workload prediction is available. We describe the three main aspects of the proposed distributed algorithm, namely, a dynamic partitioning of the search space, a distribution process based on a peer-to-peer communication framework, and a novel receiverinitiated load balancing algorithm. The effectiveness of the distributed method has been evaluated on the well-known National Cancer Institute’s HIV-screening data set, where we were able to show close-to linear speedup in a network of workstations. The proposed approach also allows for dynamic resource aggregation in a non dedicated computational environment. These features make it suitable for large-scale, multi-domain, heterogeneous environments, such as computational grids.

PARALLEL ALGORITHMS FOR MAXIMAL CLIQUES IN CIRCLE GRAPHS AND UNRESTRICTED DEPTH SEARCH

We present parallel algorithms on the BSP/CGM model, with p processors, to count and generate all the maximal cliques of a circle graph with n vertices and m edges. To count the number of all the maximal cliques, without actually generating them, our algorithm requires O(log p) communication rounds with O(nm/p) local computation time. We also present an algorithm to generate the first maximal clique in O(log p) communication rounds with O(nm/p) local computation, and to generate each one of the subsequent maximal cliques this algorithm requires O(log p) communication rounds with O(m/p) local computation. The maximal cliques generation algorithm is based on generating all maximal paths in a directed acyclic graph, and we present an algorithm for this problem that uses O(log p) communication rounds with O(m/p) local computation for each maximal path. We also show that the presented algorithms can be extended to the CREW PRAM model.

Effects in mechanical properties and structure of the soil tillage with rotary paraplow

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Effects in mechanical properties and structure of the soil after tillage with rotary paraplow

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Quasiperiodic Graphs: Structural Design, Scaling and Entropic Properties

A novel class of graphs, here named quasiperiodic, are const ructed via application of the Horizontal Visibility algorithm to the time series generated along the quasiperiodic route to chaos. We show how the hierarchy of mode-locked regions represented by the Far ey tree is inherited by their associated graphs. We are able to establish, via Renormalization Group (RG) theory, the architecture of the quasiperiodic graphs produced by irrational winding numbers with pure periodic continued fraction. And finally, we demonstrate that the RG fixed-point degree distributions are recovered via optimization of a suitably defined graph entropy

Fluoride-modified electrical properties of lead borate glasses and electrochemically induced crystallization in the glassy state

Lead fluoroborate glasses were prepared by the melt-quenching technique and characterized in terms of (micro)structural and electrical properties. The study was conducted on as prepared as well as temperature- and/or electric field-treated glass samples. The results show that, in the as-prepared glassy-state materials, electrical conductivity improved with increasing the PbF(2) glass content. This result involves both an increase of the fluoride charge carrier density and, especially, a decrease of the activation energy from a glass structure expansion improving charge carrier mobility. Moreover, for the electric field-treated glass samples, surface crystallization was observed even below the glass transition temperature. As previously proposed in literature, and shown here, the occurrence of this phenomenon arose from an electrochemically induced redox reaction at the electrodes, followed by crystallite nucleation. Once nucleated, growth of beta-PbF(2) crystallites, with the indication of incorporating reduced lead ions (Pb(+)), was both (micro)structurally and electrically detectable and analyzed. The overall crystallization-associated features observed here adapt well with the floppy-rigid model that has been proposed to further complete the original continuous-random-network model by Zachariasen for closely addressing not only glasses' structure but also crystallization mechanism. Finally, the crystallization-modified kinetic picture of the glasses' electrical properties, through application of polarization/depolarization measurements originally combined with impedance spectroscopy, was extensively explored. (c) 2008 American Institute of Physics.

Effect of the processing conditions and the addition of trans-polyoctenylene rubber on the properties of natural rubber/styrene-butadiene rubber blends

In this study, the influence of the processing conditions and the addition of trans-polyoctenylene rubber (TOR) on Mooney viscosity, tensile properties, hardness, tearing resistance, and resilience of natural rubber/styrene-butadiene rubber blends was investigated. The results obtained are explained in light of dynamic mechanical and morphological analyses. Increasing processing time produced a finer blend morphology, which resulted in an improvement in the mechanical properties. The addition of TOR involved an increase in hardness, a decrease in tear resistance, and no effect on the resilience. It resulted in a large decrease in the Mooney viscosity and a slight decrease in the tensile properties if the components of the compounds were not properly mixed. The results indicate that TOR acted more as a plasticizer than a compatibilizer. (c) 2008 Wiley Periodicals, Inc.

Alterations in energy properties of eucalyptus wood and bark subjected to torrefaction: The potential of mass loss as a synthetic indicator

Torrefaction is a mild pyrolysis process (usually up to 300 degrees C) that changes the chemical and physical properties of biomass. This process is a possible pre-treatment prior to further processes (transport, grinding, combustion, gasification, etc) to generate energy or biofuels. In this study, three eucalyptus wood species and bark were subjected to different torrefaction conditions to determine the alterations in their structural and energy properties. The most severe treatment (280 degrees C, 5 h) causes mass losses of more than 35%, with severe damage to anatomical structure, and an increase of about 27% in the specific energy content. Bark is more sensitive to heat than wood. Energy yields are always higher than mass yields, thereby demonstrating the benefits of torrefaction in concentrating biomass energy. The overall mass loss is proposed as a relevant parameter to synthesize the effect of torrefaction conditions (temperature and duration). Accordingly, all results are summarised by analytical expressions able to predict the energy properties as a function of the overall mass loss. These expressions are intended to be used in any optimization procedure, from production in the field to the final use. (c) 2010 Elsevier Ltd. All rights reserved.

Retention of the Enzymatic Activity and Product Properties During Spray Drying of Pineapple Stem Extract in Presence of Maltodextrin

The aim of this work was to investigate the effects of drying parameters on the retention of the enzymatic activity and on the physical properties of spray-dried pineapple stem extract. A Box and Behnken experimental design was used to investigate the effects of the processing parameters on the product properties. The parameters studied were the inlet temperature of drying gas (Tgi), the feed flow rate of the pineapple extract relative to evaporative capacity of the system (Ws /Wmax), and the concentration of maltodextrin added to the extract (MD). Significant effects of the processing parameters on the retention of the proteolytic activity of the powdered extract were observed. High processing temperatures lead to a product with a smaller moisture content, particle size, and lower agglomerating tendency. A product with insignificant losses of the proteolytic activity ( 10%) and low moisture content (less than 6.5%) is obtained at selected conditions.

Essential Oil of Thymus vulgaris: Preparation of Pharmaceutical Mouthwash Formulation and In Vitro Evaluation of the Bacterial Plaque-Inhibiting Properties.

Essential Oil of Thymus vulgaris: Preparation of Pharmaceutical Mouthwash Formulation and In Vitro Evaluation of the Bacterial Plaque-Inhibiting Properties. The aim of this study was to evaluate the in vitro effect of the essential oil of Thymus vulgaris (thyme) pure or incorporate in a alcohol-free pharmaceutical mouthwash formulation, against Streptococcus mutans (ATCC 25175), being determined the Minimal Inhibitory Concentration (MIC) and the effect in the bacterial plate formation. The MIC value obtained for the essential oil was 100 mu g/mL (1 %). The mouthwash pharmaceutical formulation containing commercial essential oil of T. vulgaris was preparated. Microbiological and macroscopic analysis as well as analyses for MEV confirmed the effectiveness of this new alcohol-free mouthwash formulation containing essential oil of T. vulgaris as agent with plaque-inhibiting properties and possible application in the preventive dentistry. The chemical characterization of the bioactive essential oil was accomplished by CG-MS, being verified the presence of carvacrol, p-cimene and alpha-pinene as major constituents.