Multifractal formalism for Benedicks-Carleson quadratic maps

For a positive measure set of nonuniformly expanding quadratic maps on the interval we effect a multifractal formalism, i.e., decompose the phase space into level sets of time averages of a given observable and consider the associated {\it Birkhoff spectrum} which encodes this decomposition. We derive a formula which relates the Hausdorff dimension of level sets to entropies and Lyapunov exponents of invariant probability measures, and then use this formula to show that the spectrum is continuous. In order to estimate the Hausdorff dimension from above, one has to "see" sufficiently many points. To this end, we construct a family of towers. Using these towers we establish a large deviation principle for empirical distributions, with Lebesgue as a reference measure.Comment: 25 pages, no figure, Ergodic Theory and Dynamical Systems, to appea

A modelagem mateática e suas possibilidades para a açâo pedagógica do programa etnomatemática

Neste artigo, o autor procura discutir as perspectivas sobre a possibilidade da utilização da modelagem matemática como uma ação pedagógica para o ensino e aprendizagem da matemática. Essa discussão emerge em virtude da necessidade de se vincular a modelagem matemática como uma ação pedagógica para o programa etnomatemática no ensino e aprendizagem da matemática

The Role of Extracellular Matrix Proteins on Epithelial to Mesenchymal Transition in Glioblastoma Multiforme

Glioblastoma multiforme (GBM) is the most common primary brain tumor in humans and is characterized as being highly aggressive and invasive, with the ability to locally invade different areas of the central nervous system (CNS). GBM local invasion undergoes an epithelial to mesenchmal like (EMT) process characterized by the loss of cell-cell adhesion and increased cell mobility. The EMT-like switch in GBM is triggered by a single transcription factor, Twist1, and is characterized by the loss of cell clustering, re-organization of the basement membrane, and increased cell migration. GBM invasion depends on the remodeling of the extracellular matrix (ECM) microenvironment, which is induced in part by activated matrix metalloproteinases (MMPs). MMPs have proteolytic activity, acting in the breakdown of the basement membrane (BM), and facilitating cell proliferation, adhesion, migration and angiogenesis. The progression of GBM tumor malignancy is a multistep process that involves cell-cell and cell-ECM adhesion, invasion and migration. In this study, we examined the ability of the neural ECM proteins vitronectin, fibronectin, laminin and collagen IV to trigger an EMT-like response in GBM. We found that, monolayer formation of GBM cells on purified ECM proteins exhibited the mesenchymal phenotype, but this did not lead to the induction of the transcription factor Twist1, a marker used to determine GBM invasion. On the contrary, we found that GBM cells grown on collagen IV show heightened levels of Twist without the EMT-like switch in morphologies. These findings suggest an important role for collagen IV in the process of GBM local invasion

Three approaches in the research field of ethnomodeling: emic (local), etic (global), and dialogical (glocal)

The acquisition of both emic (local) and etic (global) knowledge is an alternative goal for the implementation of ethnomodeling research. Emic knowledge is essential for an intuitive and empathic understanding of mathematical ideas, procedures, and practices developed by the members of distinct cultural groups. It is essential for conducting effective ethnographic fieldwork. Furthermore, emic knowledge is a valuable source of inspiration for etic hypotheses. Etic knowledge is essential for cross-cultural comparisons, which are based on the components of ethnology. In this regard, such comparisons demand standard units and categories to facilitate communication. Dialogical (glocal) is a third approach for ethnomodeling research that makes use of both emic and etic knowledge traditions through processes of dialogue and interaction. Ethnomodeling is defined as the study of mathematical phenomena within a culture because it is a social construct and is culturally bound. Finally, the objective of this article is to show how we have come to use a combination of emic, etic and dialogical (glocal) approaches in our work in the area of ethnomodeling, which contributes to the acquisition of a more complete understanding of mathematical practices developed by the members of distinct cultural groups

Discussing mathematical modeling coursein a long distance course

The research related to critical and reflective dimensions of mathematical modeling isseeking identity, definition, and objectives. As well, it is developing a sense of its own nature andpotential for research methods used in order to legitimize pedagogical action. It is necessary to discussthe importance of philosophical and theoretical perspectives found in critically reflective dimensionsof mathematical modeling. As well, the importance of a virtual learning environment that helpsstudents to develop critical-reflective efficiencies has become increasingly important to enable the exploration of theories related to critical mathematical modeling, distance interactions, and transactional distance by using long-distance technologies. These interactions are triggered by lessons placed on platforms, which are virtual learning environments (VLE) and that enable the use a combination of technology, teaching and the learning of specific content. By developing discusión forums and video conferences, professors and tutors are able to analyze interactions enabled by these tools, which contributed to the reflective developmentof the elaboration of mathematical models in the VLE

Sharp large deviations for some hyperbolic systems

We prove a sharp large deviation principle concerning intervals shrinking with sub-exponential speed for certain models involving the Poincar\'e map related to a Markov family for an Axiom A flow restricted to a basic set $\Lambda$ satisfying some additional regularity assumptions.Comment: arXiv admin note: substantial text overlap with arXiv:0810.112

Symmetrical freedom quilts: the ethnomathematics of ways of communication, liberation, and art

Symmetrical Freedom Quilts may be considered as links between mathematics, history, ethnomathematics, and the art of quilting. A quilt theme is a pedagogical way to integrate mathematics, art, and history in an interdisciplinary approach. This article combines an ethnomathematical-historical perspective by elaborating a history project related to the Underground Railroad. This work will allow teachers to develop classroom projects that help students to better understand geometry, especially concepts of symmetry and transformations. One of the objectives of this project is to stimulate student’s creativity and interest, because quilts may be considered as cultural and mathematical expressions of student’s daily life

Fortifying Election Security Through Poll Worker Policy

The smooth functioning of elections relies on hundreds of thousands of part-time workers across the United States to support the voting and counting process. Poll workers and other temporary election workers support all aspects of the voting process. They are responsible for setting up voting equipment, checking in voters, and assisting in the counting of ballots. To ensure the smooth functioning of an election, workers must conduct their job with integrity and discipline. Their role, and the public's trust in their role, is a cornerstone of the democratic process.Concerns are mounting that temporary election workers recruited and trained by organizations with nefarious intent may undermine election security and public trust. In a statement released in early October 2022, the Bipartisan Policy Center's Task Force on Elections condemned "any effort designed with the intent of using temporary election workers to undermine the credibility of the election ecosystem."The COVID-19 pandemic made recruitment of election workers more difficult and highlighted the importance of temporary election workers. Since then, there have been several isolated incidents in which temporary election workers attempted to undermine election administration in pursuit of partisan goals. Before Michigan's August primary, some poll workers were instructed to unplug voting equipment in the name of exposing fraud. On September 29, 2022 a Michigan poll worker was charged with falsifying records and tampering with voting equipment during the primary.To restore and maintain trust in the election system, the public must have faith that poll workers will uphold their duties and defend the election infrastructure that allows U.S. democracy to function. This explainer surveys the state of temporary election-worker policies across all 50 states, highlighting both the litany of protections in place and the gaps that remain

Un estudio etnomatemático de las esteras (Pop) sagradas de los mayas

El contexto holístico de la etnomatemáticas busca estudiar, reflejar, y comprender las relaciones existentes entre los componentes del grupo cultural a través del análisis constante de cada individuo en el propio ambiente cultural. En este contexto, los mayas utilizaron padrones geométricos llamados de esteras o Pop que se tornaron sagrados. Esos padrones eran esculpidos en piedras, utilizados como joyas y dibujados en tejidos. Algunos objetos encontrados en México y en América Central muestran que los sacerdotes mayas tomaban ciertas decisiones basadas en las esteras sagradas, pues ellas contenían significados sagrados basados en valores finales de cada padrón. Los autores demuestran aspectos etnomatemáticos de la cultura maya que están basados en las pesquisas realizadas sobre las ideas y practicas matemáticas de este pueblo