No abstract

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Abstract. The use of different mathematical tools to study biological processes is necessary to capture effects occurring at different scales. Here we study as an example the immune response to infection with the bacteria Mycobacterium tuberculosis, the causative agent of tuberculosis (TB). Immune responses are both global (lymph nodes, blood, and spleen) as well as local (site of infection) in nature. Interestingly, the immune response in TB at the site of infection results in the formation of spherical structures comprised of cells, bacteria, and effector molecules known as granulomas. In this work, we use four different mathematical tools to explore both the global immune response as well as the more local one (granuloma formation) and compare and contrast results obtained using these methods. Applying a range of approaches from continuous deterministic models to discrete stochastic ones allows us to make predictions and suggest hypotheses about the underlying biology that might otherwise go unnoticed. The tools developed and applied here are also applicable in other settings such as tumor modeling.

C oronavirus disease (COVID-19) infection, after the first case reported in Wuhan, China, on December 31, 2019 and declared a pandemic by the World Health Organization in March 2020, has climbed by September 2nd to 26,076,572 cases and 864,162 deaths worldwide.Although it has been suggested that living at high altitude could decrease the rate of coronavirus transmission and mortality from COVID-19 (Arias-Reyes et al., 2020), new studies have not confirmed this protective effect. In fact, the case-fatality rate in Peru did not change with altitude (Segovia-Juarez et al., 2020).In the United States and Mexico, populations located >2,000 m have a higher total cumulative number of COVID-19 cases and a higher mortality rate attributable to COVID-19 than those located <1,500 m (Woolcott and Bergman, 2020). This study included data up to April 13, 2020, in the United States and up to May 13, 2020, in Mexico.A recent comprehensive review calls into question whether environmental factors, particularly ambient hypoxia, may be responsible at high altitude for reducing viral transmission and mortality due to COVID-19 (Pun et al., 2020). These conflicting results need further clarification and more current data. For this, we have assessed data from Peru, a country with one of the highest per capita number of infections and mortality rate worldwide.We used data of COVID-19 cases from 1,636 districts located from 5 to 4,705 m. The data set of COVID-19 cases (N = 535,946, from March 6 to August 15, 2020) was obtained from the National Open Data Platform (MINSA, 2020). Population and altitude data were gathered from National Institute of Information and Statistics (INEI, 2019), and combined with the aforementioned data set. This afforded altitude and district population information for 509,521 positive cases, representing people living at different altitudes, and providing the possibility of studying the effect of altitude with enough power to determine statistical significance.We considered three ranges: (1) altitudes <1,000 m, (2) altitudes between 1,000 and 2,500 m, and (3) altitudes

Color is one of the most widely used features for image similarity retrieval. Most of the existing image similarity retrieval schemes employ either global or local color histogramming. In this paper, we explore the use of localized dominant hue and saturation values for color-based image similarity retrieval. This scheme results in a relatively compact representation of color images for similarity retrieval. Experimental results comparing the proposed representation with global and local color histogramming are presented to show the efficacy of the suggested scheme.