Estimating persistent Betti numbers for discrete shape analysis

Persistent Topology is an innovative way of matching topology and geometry, and it proves to be an effective mathematical tool in shape analysis. In order to express its full potential for applications, it has to interface with the typical environment of Computer Science: It must be possible to deal with a finite sampling of the object of interest, and with combinatorial representations of it. Following that idea, the main result claims that it is possible to construct a relation between the persistent Betti numbers (PBNs; also called rank invariant) of a compact, Riemannian submanifold X of R^m and the ones of an approximation U of X itself, where U is generated by a ball covering centered in the points of the sampling. Moreover we can state a further result in which, this time, we relate X with a finite simplicial complex S generated, thanks to a particular construction, by the sampling points. To be more precise, strict inequalities hold only in "blind strips'', i.e narrow areas around the discontinuity sets of the PBNs of U (or S). Out of the blind strips, the values of the PBNs of the original object, of the ball covering of it, and of the simplicial complex coincide, respectively.

Territorial assemblages and Governance : The example of the Taonaba project [Town of Abymes, Guadeloupe]

This article reports on an action research to support the urban community of Cap Excellence in Guadaloupe in its local sustainable development project. After summarizing the terms of the debate around sustainable development, and presenting the region, the search will be put back into the context of a more general approach of territorial* intelligence (TI). The limits of a local Agenda 21 in the form of a 'programmed action plan' is the chance to enhance the concept of TI with that of territorial assemblage. Our study area is the natural reserve of the Grand Cul-de-Sac Marin of Guadeloupe, the second largest biosphere reserve designated by UNESCO in the archipelago of the Petites Antilles, more specifically the implementation of the Taonaba project, whose goal is to launch an ecotourism visitors' centre, operational at the end of 2012. Based on the analysis of a large amount of data, the article describes an evaluation tool for territorial assemblages for participative territorial governance. Our results were presented to local government officials in the Urban Sustainable Development Forum, which our group organised from 2 to 4 April 2012, in the district of Abymes/Pointe-à-Pitre

Territorial assemblages and Governance : The example of the Taonaba project [Town of Abymes, Guadeloupe]

This article reports on an action research to support the urban community of Cap Excellence in Guadaloupe in its local sustainable development project. After summarizing the terms of the debate around sustainable development, and presenting the region, the search will be put back into the context of a more general approach of territorial* intelligence (TI). The limits of a local Agenda 21 in the form of a 'programmed action plan' is the chance to enhance the concept of TI with that of territorial assemblage. Our study area is the natural reserve of the Grand Cul-de-Sac Marin of Guadeloupe, the second largest biosphere reserve designated by UNESCO in the archipelago of the Petites Antilles, more specifically the implementation of the Taonaba project, whose goal is to launch an ecotourism visitors' centre, operational at the end of 2012. Based on the analysis of a large amount of data, the article describes an evaluation tool for territorial assemblages for participative territorial governance. Our results were presented to local government officials in the Urban Sustainable Development Forum, which our group organised from 2 to 4 April 2012, in the district of Abymes/Pointe-à-Pitre

Territorial assemblages and Governance : The example of the Taonaba project [Town of Abymes, Guadeloupe]

This article reports on an action research to support the urban community of Cap Excellence in Guadaloupe in its local sustainable development project. After summarizing the terms of the debate around sustainable development, and presenting the region, the search will be put back into the context of a more general approach of territorial* intelligence (TI). The limits of a local Agenda 21 in the form of a 'programmed action plan' is the chance to enhance the concept of TI with that of territorial assemblage. Our study area is the natural reserve of the Grand Cul-de-Sac Marin of Guadeloupe, the second largest biosphere reserve designated by UNESCO in the archipelago of the Petites Antilles, more specifically the implementation of the Taonaba project, whose goal is to launch an ecotourism visitors' centre, operational at the end of 2012. Based on the analysis of a large amount of data, the article describes an evaluation tool for territorial assemblages for participative territorial governance. Our results were presented to local government officials in the Urban Sustainable Development Forum, which our group organised from 2 to 4 April 2012, in the district of Abymes/Pointe-à-Pitre

On f-vectors of polytopes and matroids

Thesis (Ph.D.)--University of Washington, 2016-08

Learning representations for graph-structured socio-technical systems

The recent widespread use of social media platforms and web services has led to a vast amount of behavioral data that can be used to model socio-technical systems. A significant part of this data can be represented as graphs or networks, which have become the prevalent mathematical framework for studying the structure and the dynamics of complex interacting systems. However, analyzing and understanding these data presents new challenges due to their increasing complexity and diversity. For instance, the characterization of real-world networks includes the need of accounting for their temporal dimension, together with incorporating higher-order interactions beyond the traditional pairwise formalism. The ongoing growth of AI has led to the integration of traditional graph mining techniques with representation learning and low-dimensional embeddings of networks to address current challenges. These methods capture the underlying similarities and geometry of graph-shaped data, generating latent representations that enable the resolution of various tasks, such as link prediction, node classification, and graph clustering. As these techniques gain popularity, there is even a growing concern about their responsible use. In particular, there has been an increased emphasis on addressing the limitations of interpretability in graph representation learning. This thesis contributes to the advancement of knowledge in the field of graph representation learning and has potential applications in a wide range of complex systems domains. We initially focus on forecasting problems related to face-to-face contact networks with time-varying graph embeddings. Then, we study hyperedge prediction and reconstruction with simplicial complex embeddings. Finally, we analyze the problem of interpreting latent dimensions in node embeddings for graphs. The proposed models are extensively evaluated in multiple experimental settings and the results demonstrate their effectiveness and reliability, achieving state-of-the-art performances and providing valuable insights into the properties of the learned representations.

Simplicial Complexes From Graphs Toward Graph Persistence

Persistent homology is a branch of computational topology which uses geometry and topology for shape description and analysis. This dissertation is an introductory study to link persistent homology and graph theory, the connection being represented by various methods to build simplicial complexes from a graph. The methods we consider are the complex of cliques, of independent sets, of neighbours, of enclaveless sets and complexes from acyclic subgraphs, each revealing several properties of the underlying graph. Moreover, we apply the core ideas of persistence theory in the new context of graph theory, we define the persistent block number and the persistent edge-block number.

Albumin Is Synthesized In Epididymis And Aggregates In A High Molecular Mass Glycoprotein Complex Involved In Sperm-egg Fertilization.

The epididymis has an important role in the maturation of sperm for fertilization, but little is known about the epididymal molecules involved in sperm modifications during this process. We have previously described the expression pattern for an antigen in epididymal epithelial cells that reacts with the monoclonal antibody (mAb) TRA 54. Immunohistochemical and immunoblotting analyses suggest that the epitope of the epididymal antigen probably involves a sugar moiety that is released into the epididymal lumen in an androgen-dependent manner and subsequently binds to luminal sperm. Using column chromatography, SDS-PAGE with in situ digestion and mass spectrometry, we have identified the protein recognized by mAb TRA 54 in mouse epididymal epithelial cells. The ∼65 kDa protein is part of a high molecular mass complex (∼260 kDa) that is also present in the sperm acrosomal vesicle and is completely released after the acrosomal reaction. The amino acid sequence of the protein corresponded to that of albumin. Immunoprecipitates with anti-albumin antibody contained the antigen recognized by mAb TRA 54, indicating that the epididymal molecule recognized by mAb TRA 54 is albumin. RT-PCR detected albumin mRNA in the epididymis and fertilization assays in vitro showed that the glycoprotein complex containing albumin was involved in the ability of sperm to recognize and penetrate the egg zona pellucida. Together, these results indicate that epididymal-derived albumin participates in the formation of a high molecular mass glycoprotein complex that has an important role in egg fertilization.

Effects Of Partial Inhibition Of Respiratory Complex I On H2o 2 Production By Isolated Brain Mitochondria In Different Respiratory States.

The aim of this work was to characterize the effects of partial inhibition of respiratory complex I by rotenone on H2O2 production by isolated rat brain mitochondria in different respiratory states. Flow cytometric analysis of membrane potential in isolated mitochondria indicated that rotenone leads to uniform respiratory inhibition when added to a suspension of mitochondria. When mitochondria were incubated in the presence of a low concentration of rotenone (10 nm) and NADH-linked substrates, oxygen consumption was reduced from 45.9 ± 1.0 to 26.4 ± 2.6 nmol O2 mg(-1) min(-1) and from 7.8 ± 0.3 to 6.3 ± 0.3 nmol O2 mg(-1) min(-1) in respiratory states 3 (ADP-stimulated respiration) and 4 (resting respiration), respectively. Under these conditions, mitochondrial H2O2 production was stimulated from 12.2 ± 1.1 to 21.0 ± 1.2 pmol H2O2 mg(-1) min(-1) and 56.5 ± 4.7 to 95.0 ± 11.1 pmol H2O2 mg(-1) min(-1) in respiratory states 3 and 4, respectively. Similar results were observed when comparing mitochondrial preparations enriched with synaptic or nonsynaptic mitochondria or when 1-methyl-4-phenylpyridinium ion (MPP(+)) was used as a respiratory complex I inhibitor. Rotenone-stimulated H2O2 production in respiratory states 3 and 4 was associated with a high reduction state of endogenous nicotinamide nucleotides. In succinate-supported mitochondrial respiration, where most of the mitochondrial H2O2 production relies on electron backflow from complex II to complex I, low rotenone concentrations inhibited H2O2 production. Rotenone had no effect on mitochondrial elimination of micromolar concentrations of H2O2. The present results support the conclusion that partial complex I inhibition may result in mitochondrial energy crisis and oxidative stress, the former being predominant under oxidative phosphorylation and the latter under resting respiration conditions.

A New Platinum Complex With Tryptophan: Synthesis, Structural Characterization, Dft Studies And Biological Assays In Vitro Over Human Tumorigenic Cells.

A new platinum(II) complex with the amino acid L-tryptophan (trp), named Pt-trp, was synthesized and characterized. Elemental, thermogravimetric and ESI-QTOF mass spectrometric analyses led to the composition [Pt(C11H11N2O2)2]⋅6H2O. Infrared spectroscopic data indicate the coordination of trp to Pt(II) through the oxygen of the carboxylate group and also through the nitrogen atom of the amino group. The (13)C CP/MAS NMR spectroscopic data confirm coordination through the oxygen atom of the carboxylate group, while the (15)N CP/MAS NMR data confirm coordination of the nitrogen of the NH2 group to the metal. Density functional theory (DFT) studies were applied to evaluate the cis and trans coordination modes of trp to platinum(II). The trans isomer was shown to be energetically more stable than the cis one. The Pt-trp complex was evaluated as a cytotoxic agent against SK-Mel 103 (human melanoma) and Panc-1 (human pancreatic carcinoma) cell lines. The complex was shown to be cytotoxic over the considered cells.

Synthesis, characterization, DFT and Td-dfT study of the [Fe(mnt)(L)(t-BuNC) 2] octahedral complex (L = phen, bipy)

FeBr2 has reacted with an equivalent of mnt2- (mnt = cis-1,2-dicyanoethylene-1,2-dithiolate) and the α-diimine L (L = 1,10'-phenantroline, 2,2'-bipyridine) in THF solution, and followed by adding of t-butyl-isocyanide to give [Fe(mnt)(L)(t-BuNC)2] neutral compound. The products were characterized by infrared, UV-visible and Mössbauer spectroscopy, besides thermogravimetric and conductivity data. The geometry in the equilibrium was calculated by the density functional theory and the electronic spectrum by the time-dependent. The experimental and theoretical results in good agreement have defined an octahedral geometry with two isocyanide neighbours. The π→π* intraligand electronic transition was not observed for cis-isomers in the near-IR spectral region.

Management of a complex dentoalveolar trauma: a case report

This paper describes the case of a 12-year-old male patient who presented a severe lateral luxation of the maxillary central incisors due to a bicycle fall. Treatment involved suture of the soft tissues lacerations, and repositioning and splinting of the injured teeth, followed by endodontic treatment and periodontal surgery. After a 2-year follow-up, clinical and radiographic evaluation revealed that the incisors presented satisfactory esthetic and functional demands.

Overview of the taxonomy and of the major secondary metabolites and their biological activities related to human health of the Laurencia complex (Ceramiales, Rhodophyta) from Brazil

In Brazil, the Laurencia complex is represented by twenty taxa: Laurencia s.s. with twelve species, Palisada with four species (including Chondrophycus furcatus now that the proposal of its transference to Palisada is in process), and Osmundea and Yuzurua with two species each. The majority of the Brazilian species of the Laurencia complex have been phylogenetically analyzed by 54 rbcL sequences, including five other Rhodomelacean species as outgroups. The analysis showed that the Laurencia complex is monophyletic with high posterior probability value. The complex was separated into five clades, corresponding to the genera: Chondrophycus, Laurencia, Osmundea, Palisada, and Yuzurua. A bibliographical survey of the terpenoids produced by Brazilian species showed that only six species of Laurencia and five of Palisada (including C. furcatcus) have been submitted to chemical analysis with 48 terpenoids (47 sesquiterpenes and one triterpene) isolated. No diterpenes were found. Of the total, 23 sesquiterpenes belong to the bisabolane class and eighteen to the chamigrene type, whose biochemical precursor is bisabolane, two are derived from lauranes and four are triquinols. Despite the considerable number of known terpenes and their ecological and pharmacological importance, few experimental biological studies have been performed. In this review, only bioactivities related to human health were considered.

Astyanax hastatus Myers, 1928 (Teleostei, Characidae): a new species complex within the genus Astyanax?

Four populations of Astyanax hastatus Myers 1928 from the Guapimirim River basin (Rio de Janeiro State) were analyzed and three distinct cytotypes identified. These cytotypes presented 2n = 50 chromosomes, with 4M+8SM+10ST+28A (Cytotype A), 8M+10SM+14ST+18A (Cytotype B), 6M+8SM+4ST+32A (Cytotype C) and scanty heterochromatin, mainly located throughout pericentromeric regions of several chromosomal pairs. No homologies with the As-51 satellite DNA were observed in the three cytotypes, although all of them presented multiple 18S rDNA sites, as detected by both silver nitrate staining and FISH (fluorescent in situ hybridization). The application of the term "species complex" in Astyanax is discussed from a cytotaxonomic viewpoint.