Spectral Thresholds in the Bipartite Stochastic Block Model

We consider a bipartite stochastic block model on vertex sets $V_1$ and $V_2$, with planted partitions in each, and ask at what densities efficient algorithms can recover the partition of the smaller vertex set. When $|V_2| \gg |V_1|$, multiple thresholds emerge. We first locate a sharp threshold for detection of the partition, in the sense of the results of \cite{mossel2012stochastic,mossel2013proof} and \cite{massoulie2014community} for the stochastic block model. We then show that at a higher edge density, the singular vectors of the rectangular biadjacency matrix exhibit a localization / delocalization phase transition, giving recovery above the threshold and no recovery below. Nevertheless, we propose a simple spectral algorithm, Diagonal Deletion SVD, which recovers the partition at a nearly optimal edge density. The bipartite stochastic block model studied here was used by \cite{feldman2014algorithm} to give a unified algorithm for recovering planted partitions and assignments in random hypergraphs and random $k$-SAT formulae respectively. Our results give the best known bounds for the clause density at which solutions can be found efficiently in these models as well as showing a barrier to further improvement via this reduction to the bipartite block model.Comment: updated version, will appear in COLT 201

A discussion of a cryptographical scheme based in F-critical sets of a Latin square

This communication provides a discussion of a scheme originally proposed by Falcón in a paper entitled “Latin squares associated to principal autotopisms of long cycles. Applications in cryptography”. Falcón outlines the protocol for a cryptographical scheme that uses the F-critical sets associated with a particular Latin square to generate access levels for participants of the scheme. Accompanying the scheme is an example, which applies the protocol to a particular Latin square of order six. Exploration of the example itself, revealed some interesting observations about both the structure of the Latin square itself and the autotopisms associated with the Latin square. These observations give rise to necessary conditions for the generation of the F-critical sets associated with certain autotopisms of the given Latin square. The communication culminates with a table which outlines the various access levels for the given Latin square in accordance with the scheme detailed by Falcón.Publisher PDFPeer reviewe

Beware of the Parallel-Replacement Zombies

In this paper, the authors discuss the use of computer homework systems and describe what many students do when they are completing their work online. Strategies are provided to help students develop a more conceptual understanding of mathematics and help to avoid the number replacement method

Anti-Cancer Drugs Effect on Quasi-palindrome Mutations in Escherichia coli

Cancer is one of the world\u27s largest health problems in today’s age. The Global Burden of Disease estimates that 10 million people died as a result of cancer per year (IHME). Although there are many treatments for different types of cancer, many of the drugs used are known to have severe side effects. These known consequences include hair loss, nausea, and, unfortunately, an increase in DNA mutation, which can trigger other classes of diseases. One class of mutations that have been studied and linked to a form of cancer is Quasi-palindrome template switch mutations. Quasi-palindromes are nearly perfect inverted repeats of nucleotides able to form DNA secondary structures. These Hairpins are an example of a secondary DNA structure made by DNA repeats and are known to block the DNA replication fork (VOINEAGU et al. 2008). Once DNA replication is blocked by these secondary DNA structures, the DNA replication fork needs to find a solution to continue the replication process. At some frequency, DNA polymerase (responsible for replicating the DNA) can use alternative DNA strands as templates to make more DNA. One alternative method is called “Template-switching”, and it results in a mutation that creates a perfect palindrome from a quasi-palindromic sequence. Previous work has linked anti-cancer drugs such as 5-azacytidine to an increase of QP mutations (Laranjo 2018). Therefore, I am interested in analyzing other anti-cancer drugs and their potential to cause QP mutations. Using an FDA approved drug library, with over 300 different drugs, we will select anti-cancer drugs to screen for QP mutators. We have constructed a QP reporter in E. coli that is specific for QP mutations (Laranjo 2017). To understand the effect of anti-cancer drugs during DNA replication is critical to give us an understanding of potential side effects for patients undergoing chemotherapy

Living Situation and Physical Activity in the COVID-19 Pandemic Among Private University Students

Physical activity levels among college students in private institutions were significantly altered by the COVID-19 pandemic. With COVID-19’s impact on universities, many students experienced transition, including a change in living situation. Behaviors in college help establish life-long habits that can determine health outcomes, so it’s important to investigate any declines in physical activity observed during the pandemic. PURPOSE: The purpose of this study was to assess differences in physical activity based on living situation among 18- to 25-year-old private university students during the COVID-19 pandemic. METHODS: Adults (n=109) between 18- and 25-years-old in the greater Houston area completed an online survey, which included the International Physical Activity Questionnaire – Short Form. Independent samples T-tests examined MET-minute differences based on living situation. RESULTS: Students living with versus without a parent/guardian attained similar activity levels (t(107) = -.114, p = .910) before the pandemic, but students living with a parent/guardian engaged in significantly less activity (t(107) = 2.04, p = .044) during the pandemic. CONCLUSION: The pandemic presented a strong obstacle to physical activity participation among private university students. Students living with a parent/guardian during this time saw an even more significant decrease in physical activity. Based on these findings, targeted interventions should be made to increase the physical activity of college students during COVID-19, especially for those living at home with a parent or guardian

Physical Activity Independently Predicts Perceived Stress During the COVID-19 Pandemic in Private University Students

International Journal of Exercise Science 15(7): 1680-1691, 2022. Physical activity has significantly declined during the COVID-19 pandemic. Declines in physical activity have correlated with increased levels of perceived stress, though studies examining physical activity and stress have failed to account for critical confounds. The present study aims to determine whether physical activity independently predicts perceived stress in students attending private four-year universities. Physical activity, socioeconomic status, resilience, gender, and perceived stress data were collected from 85 students and used in a multiple linear regression analysis. The regression model accounted for 43.5% of the variance in perceived stress (R2 = .462, p \u3c .001). Total physical activity significantly and inversely predicted perceived stress (β = –.229, p = .007) in students irrespective of other covariates. Socioeconomic status, resilience, and gender also independently and significantly predicted perceived stress. Findings should be leveraged by university staff to promote psychological well-being and wholistic health initiatives incorporating physical activity as a primary and modifiable component

Living Situation and Physical Activity in the COVID-19 Pandemic Among American Private University Students

International Journal of Exercise Science 15(4): 1064-1074, 2022. Many university students experienced changes during the COVID-19 pandemic, including potential changes in physical activity (PA) levels and living situation. As PA behaviors in young adulthood help establish life-long habits and future health outcomes, the purpose of this study was to investigate overall change in PA, as well as change in PA due to living situation, among private university students during the COVID-19 pandemic. Private university students (n = 109) between 18 and 25 years of age completed an online survey that included the International Physical Activity Questionnaire – Short Form. T-tests examined changes in overall time spent in PA from before to during the COVID-19 pandemic, and the differences in MET-minute distributions between groups. Students performed significantly less activity during the COVID-19 pandemic than before (t(108) = 3.51, p = .001, d = 0.493), with 70.6% of all students meeting exercise recommendations before the pandemic and 51.4% after. Students living with vs. without a parent/guardian attained similar PA levels (t(107) = -.114, p = .910) before the pandemic (73.1% vs. 69.9%, respectively), but students living with a parent/guardian engaged in significantly less PA (t(107) = 2.04, p = .044, d = 0.475) than those living without a parent/guardian during the pandemic (37.5% vs. 57.1%, respectively). The declines in PA suggest the need for targeted interventions and education among private university students. In order to maximize the health benefits of PA, it is crucial that activity engagement return to at least pre-COVID-19 levels