Class Notes for Math 905: Commutative Algebra, Instructor Sylvia Wiegand

Topics include: Rings, ideals, algebraic sets and affine varieties, modules, localizations, tensor products, intersection multiplicities, primary decomposition, the Nullstellensatz

Blocking of Connexin-Mediated Communication Promotes Neuroprotection during Acute Degeneration Induced by Mechanical Trauma

Accruing evidence indicates that connexin (Cx) channels in the gap junctions (GJ) are involved in neurodegeneration after injury. However, studies using KO animal models endowed apparently contradictory results in relation to the role of coupling in neuroprotection. We analyzed the role of Cx-mediated communication in a focal lesion induced by mechanical trauma of the retina, a model that allows spatial and temporal definition of the lesion with high reproducibility, permitting visualization of the focus, penumbra and adjacent areas. Cx36 and Cx43 exhibited distinct gene expression and protein levels throughout the neurodegeneration progress. Cx36 was observed close to TUNEL-positive nuclei, revealing the presence of this protein surrounding apoptotic cells. The functional role of cell coupling was assessed employing GJ blockers and openers combined with lactate dehydrogenase (LDH) assay, a direct method for evaluating cell death/viability. Carbenoxolone (CBX), a broad-spectrum GJ blocker, reduced LDH release after 4 hours, whereas quinine, a Cx36-channel specific blocker, decreased LDH release as early as 1 hour after lesion. Furthermore, analysis of dying cell distribution confirmed that the use of GJ blockers reduced apoptosis spread. Accordingly, blockade of GJ communication during neurodegeneration with quinine, but not CBX, caused downregulation of initial and effector caspases. To summarize, we observed specific changes in Cx gene expression and protein distribution during the progress of retinal degeneration, indicating the participation of these elements in acute neurodegeneration processes. More importantly, our results revealed that direct control of GJ channels permeability may take part in reliable neuroprotection strategies aimed to rapid, fast treatment of mechanical trauma in the retina.

Comparison between multiple sets and half-pyramid resistance exercise bouts for muscle damage profile

The present study compared the changes in markers of muscle damage after bouts of resistance exercise employing the Multiple-sets (MS) and Half-pyramid (HP) training systems. Ten healthy men (26.1 +/- 6.3 years), who had been involved in regular resistance training, performed MS and HP bouts, 14 days apart, in a randomised, counter-balanced manner. For the MS bout, participants performed three sets of maximum repetitions at 75%-1RM (i.e. 75% of a One Repetition Maximum) for the three exercises, starting with the bench press, followed by pec deck and decline bench press. For the HP bout, the participants performed three sets of maximum repetitions with 67%-1RM, 74%-1RM and 80%-1RM for the first, second and third sets, respectively, for the same three exercise sequences as the MS bout. The total volume of load lifted was equated between both bouts. Muscle soreness, plasma creatine kinase (CK) activity, myoglobin (Mb) and C-reactive protein (CRP) concentrations were assessed before and for three days after each exercise bout, and the changes over time were compared between MS and HP using two-way repeated measures ANOVA. Muscle soreness developed significantly (P<0.01) after both bouts, but no significant difference was observed between MS and HP. Plasma CK activity and Mb concentration increased significantly (P<0.01) without significant differences between bouts, and CRP concentration did not change significantly after either bout. These results suggest that the muscle damage profile is similar for MS and HP, probably due to the similar total volume of load lifted.

Parasites in the neighbourhood: Interactions of the mistletoe Phoradendron affine (Viscaceae) with its dispersers and hosts in urban areas of Brazil

Mistletoes constitute an important food resource for animals in many ecosystems. However, these plants are considered pests in urban areas because of deleterious effects they have on the host trees. Studies in urban areas were mostly focused on listing host species or procedures to control the "pest". In this sense, broader studies including several aspects of mistletoes ecology in urban ecosystems are still missing. We studied the interaction of the mistletoe, Phoradendron affine, with its dispersers and hosts in two urban sites in Uberlandia, Brazil. Phoradendron affine fruits were consumed almost exclusively by Euphonia chlorotica, which was crucial for seed germination. Parasitism was recorded in five hosts, two native (Handroanthus chrysotrichus and Tabebuia roseoalba) and three exotic species (Spathodea campanulata, Ligustrum lucidum and Melia azedarach). Mistletoes were found parasitizing larger host trees, a trend commonly reported for mistletoe-host interaction. Mistletoe seed germination was not affected by the trees species, whether host or non-host, but the radicle of germinated seeds could not penetrate the bark and seedlings invariably died in non-host species. We found a high prevalence of parasitism in our study, in comparison to what previous studies reported for natural areas. The spatial distribution of the hosts and high light incidence on isolated host trees may lead to this high prevalence in urban areas. Rather than eradicated, mistletoes in urban areas should be ecologically managed and their importance for bird species conservation must be considered. More studies to determine which bird species are favoured by mistletoe presence in urban areas will be essential for, this purpose. (C) 2012 Elsevier GmbH. All rights reserved.

TRANSITIVITY AND ROTATION SETS WITH NONEMPTY INTERIOR FOR HOMEOMORPHISMS OF THE 2-TORUS

We show that if f is a homeomorphism of the 2-torus isotopic to the identity and its lift (f) over tilde is transitive, or even if it is transitive outside the lift of the elliptic islands, then (0,0) is in the interior of the rotation set of (f) over tilde. This proves a particular case of Boyland's conjecture.

Tests of one Brazilian facial reconstruction method using three soft tissue depth sets and familiar assessors

Facial reconstruction is a method that seeks to recreate a person's facial appearance from his/her skull. This technique can be the last resource used in a forensic investigation, when identification techniques such as DNA analysis, dental records, fingerprints and radiographic comparison cannot be used to identify a body or skeletal remains. To perform facial reconstruction, the data of facial soft tissue thickness are necessary. Scientific literature has described differences in the thickness of facial soft tissue between ethnic groups. There are different databases of soft tissue thickness published in the scientific literature. There are no literature records of facial reconstruction works carried out with data of soft tissues obtained from samples of Brazilian subjects. There are also no reports of digital forensic facial reconstruction performed in Brazil. There are two databases of soft tissue thickness published for the Brazilian population: one obtained from measurements performed in fresh cadavers (fresh cadavers' pattern), and another from measurements using magnetic resonance imaging (Magnetic Resonance pattern). This study aims to perform three different characterized digital forensic facial reconstructions (with hair, eyelashes and eyebrows) of a Brazilian subject (based on an international pattern and two Brazilian patterns for soft facial tissue thickness), and evaluate the digital forensic facial reconstructions comparing them to photos of the individual and other nine subjects. The DICOM data of the Computed Tomography (CT) donated by a volunteer were converted into stereolitography (STL) files and used for the creation of the digital facial reconstructions. Once the three reconstructions were performed, they were compared to photographs of the subject who had the face reconstructed and nine other subjects. Thirty examiners participated in this recognition process. The target subject was recognized by 26.67% of the examiners in the reconstruction performed with the Brazilian Magnetic Resonance Pattern, 23.33% in the reconstruction performed with the Brazilian Fresh Cadavers Pattern and 20.00% in the reconstruction performed with the International Pattern, in which the target-subject was the most recognized subject in the first two patterns. The rate of correct recognitions of the target subject indicate that the digital forensic facial reconstruction, conducted with parameters used in this study, may be a useful tool. (C) 2011 Elsevier Ireland Ltd. All rights reserved.

Sets of probability distributions, independence, and convexity

This paper analyzes concepts of independence and assumptions of convexity in the theory of sets of probability distributions. The starting point is Kyburg and Pittarelli's discussion of "convex Bayesianism" (in particular their proposals concerning E-admissibility, independence, and convexity). The paper offers an organized review of the literature on independence for sets of probability distributions; new results on graphoid properties and on the justification of "strong independence" (using exchangeability) are presented. Finally, the connection between Kyburg and Pittarelli's results and recent developments on the axiomatization of non-binary preferences, and its impact on "complete" independence, are described.

Modeling and measuring the spatial relation "along": Regions, contours and fuzzy sets

The analysis of spatial relations among objects in an image is an important vision problem that involves both shape analysis and structural pattern recognition. In this paper, we propose a new approach to characterize the spatial relation along, an important feature of spatial configurations in space that has been overlooked in the literature up to now. We propose a mathematical definition of the degree to which an object A is along an object B, based on the region between A and B and a degree of elongatedness of this region. In order to better fit the perceptual meaning of the relation, distance information is included as well. In order to cover a more wide range of potential applications, both the crisp and fuzzy cases are considered. In the crisp case, the objects are represented in terms of 2D regions or ID contours, and the definition of the alongness between them is derived from a visibility notion and from the region between the objects. However, the computational complexity of this approach leads us to the proposition of a new model to calculate the between region using the convex hull of the contours. On the fuzzy side, the region-based approach is extended. Experimental results obtained using synthetic shapes and brain structures in medical imaging corroborate the proposed model and the derived measures of alongness, thus showing that they agree with the common sense. (C) 2011 Elsevier Ltd. All rights reserved.

EXAM-S: an Analysis tool for Multi-Domain Policy Sets

As distributed collaborative applications and architectures are adopting policy based management for tasks such as access control, network security and data privacy, the management and consolidation of a large number of policies is becoming a crucial component of such policy based systems. In large-scale distributed collaborative applications like web services, there is the need of analyzing policy interactions and integrating policies. In this thesis, we propose and implement EXAM-S, a comprehensive environment for policy analysis and management, which can be used to perform a variety of functions such as policy property analyses, policy similarity analysis, policy integration etc. As part of this environment, we have proposed and implemented new techniques for the analysis of policies that rely on a deep study of state of the art techniques. Moreover, we propose an approach for solving heterogeneity problems that usually arise when considering the analysis of policies belonging to different domains. Our work focuses on analysis of access control policies written in the dialect of XACML (Extensible Access Control Markup Language). We consider XACML policies because XACML is a rich language which can represent many policies of interest to real world applications and is gaining widespread adoption in the industry.

Processi di deposizione di blocking layers di TiO2 per Dye - Sensitized Solar Cells (DSSC)

Le Dye – Sensitized Solar Cells (DSSC) sono attualmente considerate tra le alternative più promettenti al fotovoltaico tradizionale. I ridotti costi di produzione e l’elevata versatilità di utilizzo rappresentano i punti di forza di questi dispositivi innovativi. Ad oggi la ricerca è concentrata prevalentemente sull’incremento delle prestazioni delle DSSC, ottenibile solamente attraverso un miglioramento delle funzioni dei singoli componenti e dell’interazione sinergica tra questi. Tra i componenti, ha recentemente assunto particolare interesse il blocking layer (BL), costituito generalmente da un film sottile di TiO2 depositato sulla superficie dell’anodo (FTO) e in grado di ottimizzare i fenomeni all’interfaccia FTO/TiO2/elettrolita. Nel corso di questo lavoro di tesi si è rivolta l’attenzione prevalentemente sulle caratteristiche del BLs (ad esempio proprietà morfologico – strutturali) cercando di mettere in correlazione il processo di deposizione con le caratteristiche finali del film ottenuto. A questo scopo è stato ottimizzato un processo di deposizione dei film via spin coating, a partire da soluzioni acquosa o alcolica di precursore (TiCl4). I film ottenuti sono stati confrontati con quelli depositati tramite un processo di dip coating riportato in letteratura. I BLs sono stati quindi caratterizzati tramite microscopia (SEM – AFM), spettrofotometria (UV.- Vis) e misure elettrochimiche (CV – EIS). I risultati ottenuti hanno messo in evidenza come i rivestimenti ottenuti da soluzione acquosa di precursore, indipendentemente dalla tecnica di deposizione utilizzata (spin coating o dip coating) diano origine a film disomogenei e scarsamente riproducibili, pertanto non idonei per l’applicazione nelle DSSC. Viceversa, i BLs ottenuti via spin coating dalla soluzione alcolica di TiCl4 sono risultati riproducibili, omogenei, e uniformemente distribuiti sulla superficie di FTO. Infine, l’analisi EIS ha in particolare evidenziato un effettivo aumento della resistenza al trasferimento di carica tra elettrodo FTO ed elettrolita in presenza di questi BLs, fenomeno generalmente associato ad un efficace blocking effect.

An alternative blocking layer for titanium dioxide (TiO 2) solar cell applications

In hybrid organic solar cells a blocking layer between transparent electrode and nanocrystalline titania particles is essential to prevent short-circuiting and current loss through recombination at the electrode interface. Here the preparation of a uniform hybrid blocking layer which is composed of conducting titania nanoparticles embedded in an insulating polymer derived ceramic is presented. This blocking layer is prepared by sol-gel chemistry where an amphiphilic block copolymer is used as a templating agent. A novel poly(dimethylsiloxane) containing amphiphilic block copolymer poly(ethyleneglycol)methylethermethacrylate-block-poly(dimethylsiloxane)-block-poly(ethyleneglycol)methylethermethacrylate has been synthesized to act as the templating agent. Plasma treatment uncovered titania surface from any polymer. Annealing at 450°C under nitrogen resulted in anatase titania with polymer derived silicon oxycarbide ceramic. Electrical characterization by conductive scanning probe microscopy experiments revealed a percolating titania network separated by an insulating ceramic matrix. Scanning Kelvin probe force microscopy showed predominant presence of titania particles on the surface creating a large surface area for dye absorption. The uniformity of the percolating structures was proven by microbeam grazing incidence small angle x-ray scattering. First applications in hybrid organic solar cells in comparison with conventional titanium dioxide blocking layer containing devices revealed 15 fold increases in corresponding efficiencies. Poly(dimethylsiloxane)-block-poly(ethyleneglycol)methylethermethacrylate and poly(ethyleneoxide)-poly(dimethylsiloxane)methylmethacrylate diblock copolymers were also synthesized. Their titania nanocomposite films were compared with the integrated blocking layer. Liner poly(ethyleneoxide) containing diblock copolymer resulted in highly ordered foam like structures. The effect of heating temperature rise to 600°C and 1000°C on titania morphology was investigated by scanning electron and force microscopy and x-ray scattering. Sol-gel contents, hydrochloric acid, titania precursor and amphiphilic triblock copolymer were altered to see their effect on titania morphology. Increase in block copolymer content resulted in titania particles of diameter 15-20 nm.

Application of a hybrid blocking layer in dye-sensitized solar cells

In dye-sensitized solar cells a blocking layer between the transparent electrode and the mesoporous titanium dioxide film is used to prevent short-circuits between the hole-conductor and the front electrode. The conventional approach is to use a compact layer of titanium dioxide prepared by spin coating or spray pyrolysis. The thickness of the blocking layer is critical. On one hand, the layer has to be thick enough to cover the rough substrate completely. On the other hand, the serial resistance increases with increasing film thickness, because the layer acts as an ohmic resistance itself. In this thesis an amphiphilic diblock copolymer is used as a functional template to produce an alternative, hybrid blocking layer. The hybrid blocking layer is thinner than the conventional, compact titanium dioxide film and thereby possesses a higher conductivity. Still, this type of blocking layer covers the rough electrode material completely and avoids current loss through charge recombination. The novel blocking layer is prepared using a tailored, amphiphilic block copolymer in combination with sol-gel chemistry. While the hydrophilic poly(ethylene oxide) part of the polymer coordinates a titanium dioxide precursor to form a percolating network of titania particles, the hydrophobic poly(dimethylsiloxane) part turns into an insulating ceramic layer. With this technique, crack-free films with a thickness down to 24 nm are obtained. The presence of a conductive titanium dioxide network for current flow, which is embedded in an insulating ceramic material, is validated by conductive scanning force microscopy. This is the first time that such a hybrid blocking layer is implemented in a solar cell. With this approach the efficiency could be increased up to 27 % compared to the conventional blocking layer. Thus, it is demonstrated that the hybrid blocking layer represents a competitive alternative to the classical approach.

Software tools and efficient algorithms for the feature detection, feature tracking, event localization, and visualization of large sets of atmospheric data

Data sets describing the state of the earth's atmosphere are of great importance in the atmospheric sciences. Over the last decades, the quality and sheer amount of the available data increased significantly, resulting in a rising demand for new tools capable of handling and analysing these large, multidimensional sets of atmospheric data. The interdisciplinary work presented in this thesis covers the development and the application of practical software tools and efficient algorithms from the field of computer science, aiming at the goal of enabling atmospheric scientists to analyse and to gain new insights from these large data sets. For this purpose, our tools combine novel techniques with well-established methods from different areas such as scientific visualization and data segmentation. In this thesis, three practical tools are presented. Two of these tools are software systems (Insight and IWAL) for different types of processing and interactive visualization of data, the third tool is an efficient algorithm for data segmentation implemented as part of Insight.Insight is a toolkit for the interactive, three-dimensional visualization and processing of large sets of atmospheric data, originally developed as a testing environment for the novel segmentation algorithm. It provides a dynamic system for combining at runtime data from different sources, a variety of different data processing algorithms, and several visualization techniques. Its modular architecture and flexible scripting support led to additional applications of the software, from which two examples are presented: the usage of Insight as a WMS (web map service) server, and the automatic production of a sequence of images for the visualization of cyclone simulations. The core application of Insight is the provision of the novel segmentation algorithm for the efficient detection and tracking of 3D features in large sets of atmospheric data, as well as for the precise localization of the occurring genesis, lysis, merging and splitting events. Data segmentation usually leads to a significant reduction of the size of the considered data. This enables a practical visualization of the data, statistical analyses of the features and their events, and the manual or automatic detection of interesting situations for subsequent detailed investigation. The concepts of the novel algorithm, its technical realization, and several extensions for avoiding under- and over-segmentation are discussed. As example applications, this thesis covers the setup and the results of the segmentation of upper-tropospheric jet streams and cyclones as full 3D objects. Finally, IWAL is presented, which is a web application for providing an easy interactive access to meteorological data visualizations, primarily aimed at students. As a web application, the needs to retrieve all input data sets and to install and handle complex visualization tools on a local machine are avoided. The main challenge in the provision of customizable visualizations to large numbers of simultaneous users was to find an acceptable trade-off between the available visualization options and the performance of the application. Besides the implementational details, benchmarks and the results of a user survey are presented.

Fractal sets and their applications in medicine

La geometria euclidea risulta spesso inadeguata a descrivere le forme della natura. I Frattali, oggetti interrotti e irregolari, come indica il nome stesso, sono più adatti a rappresentare la forma frastagliata delle linee costiere o altri elementi naturali. Lo strumento necessario per studiare rigorosamente i frattali sono i teoremi riguardanti la misura di Hausdorff, con i quali possono definirsi gli s-sets, dove s è la dimensione di Hausdorff. Se s non è intero, l'insieme in gioco può riconoscersi come frattale e non presenta tangenti e densità in quasi nessun punto. I frattali più classici, come gli insiemi di Cantor, Koch e Sierpinski, presentano anche la proprietà di auto-similarità e la dimensione di similitudine viene a coincidere con quella di Hausdorff. Una tecnica basata sulla dimensione frattale, detta box-counting, interviene in applicazioni bio-mediche e risulta utile per studiare le placche senili di varie specie di mammiferi tra cui l'uomo o anche per distinguere un melanoma maligno da una diversa lesione della cute.