Realizations of Indecomposable Persistence Modules of Arbitrarily Large Dimension

While persistent homology has taken strides towards becoming a widespread tool for data analysis, multidimensional persistence has proven more difficult to apply. One reason is the serious drawback of no longer having a concise and complete descriptor analogous to the persistence diagrams of the former. We propose a simple algebraic construction to illustrate the existence of infinite families of indecomposable persistence modules over regular grids of sufficient size. On top of providing a constructive proof of representation infinite type, we also provide realizations by topological spaces and Vietoris-Rips filtrations, showing that they can actually appear in real data and are not the product of degeneracies

META ANALISIS PENGARUH MODEL PEMBELAJARAN BERBASIS PROYEK TERHADAP KEMAMPUAN MATEMATIS SISWA

Project based learning is a type of learning that will be researched to measure the effect on students’ mathematical abilities. Every project-based learning analysis on mathematical skills may allow distinct effects for every aspect, whether mathematical skills components, different educational level, and teaching materials. Studies related to project-based learning researched and developed more and more, with the result that require reassessment from previous researches to conclude the accurate result. The goal of this research is to represent the effect of project-based model learning on the students’ mathematical ability altogether, each mathematical skills element, educational level component, and teaching materials component. The population of this study is researches regarding the effect of project-based learning model on students’ mathematical abilities published between 2015 to 2022. By data coding, 22 studies have been earned that fulfil the indicator. The data analysis technique uses a large effect size analysis. The outcome of this study is that the influence project based learning model on mathematical ability altogether has an exceptional effect with the effect size value of 1,32, the effect on mathematical ability aspect has an exceptional effect on comprehension mathematical ability with the effect size value of 2,05, the effect on educational level element has an exceptional effect on the college level with effect size value of 1,52, and the effect on teaching materials has an exceptional effect on algebraic material with effect size value of 3,93

Sparse Automatic Differentiation for Large-Scale Computations Using Abstract Elementary Algebra

Most numerical solvers and libraries nowadays are implemented to use mathematical models created with language-specific built-in data types (e.g. real in Fortran or double in C) and their respective elementary algebra implementations. However, built-in elementary algebra typically has limited functionality and often restricts flexibility of mathematical models and analysis types that can be applied to those models. To overcome this limitation, a number of domain-specific languages with more feature-rich built-in data types have been proposed. In this paper, we argue that if numerical libraries and solvers are designed to use abstract elementary algebra rather than language-specific built-in algebra, modern mainstream languages can be as effective as any domain-specific language. We illustrate our ideas using the example of sparse Jacobian matrix computation. We implement an automatic differentiation method that takes advantage of sparse system structures and is straightforward to parallelize in MPI setting. Furthermore, we show that the computational cost scales linearly with the size of the system.Comment: Submitted to ACM Transactions on Mathematical Softwar

Application of the ex-Gaussian function to the effect of the word blindness suggestion on Stroop task performance suggests no word blindness

The aim of the present paper was to apply the ex-Gaussian function to data reported by Parris et al. (2012) given its utility in studies involving the Stroop task. Parris et al. showed an effect of the word blindness suggestion when Response-Stimulus Interval (RSI) was 500 ms but not when it was 3500 ms. Analysis revealed that: (1) The effect of the suggestion on interference is observed in μ, supporting converging evidence indicating the suggestion operates over response competition mechanisms; and, (2) Contrary to Parris et al. an effect of the suggestion was observed in μ when RSI was 3500 ms. The reanalysis of the data from Parris et al. (2012) supports the utility of ex-Gaussian analysis in revealing effects that might otherwise be thought of as absent. We suggest that word reading itself is not suppressed by the suggestion but instead that response conflict is dealt with more effectively. © 2013 Parris, Dienes and Hodgson