Unbiased Monte Carlo estimate of stochastic differential equations expectations

We develop a pure Monte Carlo method to compute $E(g(X_T))$ where $g$ is a bounded and Lipschitz function and $X_t$ an Ito process. This approach extends a previously proposed method to the general multidimensional case with a SDE with varying coefficients. A variance reduction method relying on interacting particle systems is also developped.Comment: 32 pages, 14 figure

Clustering Plasmodium falciparum Genes to their Functional Roles Using k-means

We developed recently a new and novel Metric Matrics k-means (MMk-means) clustering algorithm to cluster genes to their functional roles with a view of obtaining further knowledge on many P. falciparum genes. To further pursue this aim, in this study, we compare three different k-means algorithms (including MMk-means) results from an in-vitro microarray data (Le Roch et al., Science, 2003) with the classification from an in-vivo microarray data (Daily et al., Nature, 2007) in other to perform a comparative functional classification of P. falciparum genes and further validate the effectiveness of our MMk-means algorithm. Results from this study indicate that the resulting distribution of the comparison of the three algorithms’ in vitro clusters against the in vivo clusters are similar thereby authenticating our MMk-means method and its effectiveness. However, Daily et al. claim that the physiological state (the environmental stress response) of P. falciparum in selected malaria-infected patients observed in one of their clusters can not be found in any in-vitro clusters is not true as our analysis reveal many in-vitro clusters representation in this cluster

Interview with Clare Cinelli

Clare Cinelli was born in Elk Grove, IL and has since lived in Roselle, IL. After entering Lake Park High School, she began to work for Oberweis Dairy ice-cream shop and also in a nursing home. Later that year, she transitioned to working for Levis as a retail employee until 2017. Between 2016 and 2017 Cinelli volunteered for the Special Olympics program and in 2017 she began to work for Anthopologie as a retail employee, continuing there for another 2 years. In 2019 she received a promotion from Anthopologie that made her into a 19-year-old manager. When Cinelli was hired at Anthropologie she also began attending Columbia College as an advertising major and she started selling handmade jewelry at the Columbia Shop. After spending two years pursuing her advertising degree, Cinelli changed her major to Design, a passion she has had all through high school. More specifically, she is pursing a degree in graphic design which she plans to obtain in 2021. Cinelli was forced to stay away from campus due to the global spread of the virus COVID-19. During this time Cinelli was also put on furlough with Anthopologie and had to seek unemployment. Despite the challenges Clare was able to successfully complete the 2020 school year with her grades unaffected.https://digitalcommons.colum.edu/capturingquarantine/1015/thumbnail.jp

Reducing the Time Requirement of k-Means Algorithm

Traditional k-means and most k-means variants are still computationally expensive for large datasets, such as microarray data, which have large datasets with large dimension size d. In k-means clustering, we are given a set of n data points in ddimensional space Rd and an integer k. The problem is to determine a set of k points in Rd, called centers, so as to minimize the mean squared distance from each data point to its nearest center. In this work, we develop a novel k-means algorithm, which is simple but more efficient than the traditional k-means and the recent enhanced k-means. Our new algorithm is based on the recently established relationship between principal component analysis and the k-means clustering. We provided the correctness proof for this algorithm. Results obtained from testing the algorithm on three biological data and six non-biological data (three of these data are real, while the other three are simulated) also indicate that our algorithm is empirically faster than other known k-means algorithms. We assessed the quality of our algorithm clusters against the clusters of a known structure using the Hubert-Arabie Adjusted Rand index (ARIHA). We found that when k is close to d, the quality is good (ARIHA.0.8) and when k is not close to d, the quality of our new k-means algorithm is excellent (ARIHA.0.9). In this paper, emphases are on the reduction of the time requirement of the k-means algorithm and its application to microarray data due to the desire to create a tool for clustering and malaria research. However, the new clustering algorithm can be used for other clustering needs as long as an appropriate measure of distance between the centroids and the members is used. This has been demonstrated in this work on six non-biological data