The period polynomial rf(z) for an even weight k ≥ 4 newform f ∈ Sk(Γ0(N)) is the generating function for the critical values of L(f, s). It has a functional equation relating rf(z) to rf(−1Nz). We prove the Riemann hypothesis for these polynomials: that the zeros of rf(z) lie on the circle ∣∣z∣∣=1/N‾‾√. We prove that these zeros are equidistributed when either k or N is large.
We describe two sets of courses designed to enhance the mathematical, statistical, and computational training of life science undergraduates at Emory College. The first course is an introductory sequence in differential and integral calculus, modeling with differential equations, probability, and inferential statistics. The second is an upper-division course in computational neuroscience. We provide a description of each course, detailed syllabi, examples of content, and a brief discussion of the main issues encountered in developing and offering the courses.
Isocitrate dehydrogenase (IDH) plays an indispensable role in the tricarboxylic acid cycle, and IDH mutations are present in nearly 75% of glioma and 20% of acute myeloid leukemia. One IDH1R132H inhibitor (clomifene citrate) was found by virtual screening method, which can selectively suppress mutant enzyme activities in vitro and in vivo with a dose-dependent manner. The molecular docking indicated that clomifene occupied the allosteric site of the mutant IDH1. Enzymatic kinetics also demonstrated that clomifene inhibited mutant enzyme in a non-competitive manner. Moreover, knockdown of mutant IDH1 in HT1080 cells decreased the sensitivity to clomifene. In vivo studies indicated that clomifene significantly suppressed the tumor growth of HT1080-bearing CB-17/Icr-scid mice with oral administration of 100 mg/ kg and 50 mg/kg per day. In short, our findings highlight clomifene may have clinical potential in tumor therapies as a safe and effective inhibitor of mutant IDH1.
Introduction: Coronary stenosis due to atherosclerosis restricts blood flow. Stenosis progression would lead to increased clinical risk such as heart attack. Although many risk factors were found to contribute to atherosclerosis progression, factors associated with fatigue is underemphasized. Our goal is to investigate the relationship between fatigue and stenosis progression based on in vivo intravascular ultrasound (IVUS) images and finite element models.
Methods: Baseline and follow-up in vivo IVUS and angiography data were acquired from seven patients using Institutional Review Board approved protocols with informed consent obtained. Three hundred and five paired slices at baseline and follow-up were matched and used for plaque modeling and analysis. IVUS-based thin-slice models were constructed to obtain the coronary biomechanics and stress/strain amplitudes (stress/strain variations in one cardiac cycle) were used as the measurement of fatigue. The change of lumen area (DLA) from baseline to follow-up were calculated to measure stenosis progression. Nineteen morphological and biomechanical factors were extracted from 305 slices at baseline. Correlation analyses of these factors with DLA were performed. Random forest (RF) method was used to fit morphological and biomechanical factors at baseline to predict stenosis progression during follow-up.
Results: Significant correlations were found between stenosis progression and maximum stress amplitude, average stress amplitude and average strain amplitude (p < 0.05). After factors selection implemented by random forest (RF) method, eight morphological and biomechanical factors were selected for classification prediction of stenosis progression. Using eight factors including fatigue, the overall classification accuracy, sensitivity and specificity of stenosis progression prediction with RF method were 83.61%, 86.25% and 80.69%, respectively.
The objectives of this study were to estimate the prevalence of concurrent alcohol and substance use among patients living with HIV/HCV co-infection and to compare demographic and clinical characteristics of those with concurrent alcohol and substance to those with alcohol or substance use, and to those who were abstinent. We conducted an analysis of patient reported outcomes data of patients living with HIV/HCV co-infection (n = 327) who transitioned from primary care to sub-specialty care for evaluation of candidacy for HCV treatment at a university-affiliated HIV Clinic. The prevalence of self-reported concurrent alcohol and substance use was 33%. A higher proportion of those with concurrent alcohol and substance use were currently smoking tobacco, and those who were abstinent had higher ratings of health-related quality of life compared to those with alcohol or substance use. To reduce patients’ risk for progression to advanced stages of HIV, HCV, and liver-related disease due to continued alcohol and substance and tobacco use, social workers and other health care professionals are encouraged to develop and implement intervention strategies to assist patients living with HIV/HCV co-infection in efforts to achieve behavioral change.
In response to the call of BIO2010 for integrating quantitative skills into undergraduate biology education, 30 Howard Hughes Medical Institute (HHMI) Program Directors at the 2006 HHMI Program Directors Meeting established a consortium to investigate, implement, develop, and disseminate best practices resulting from the integration of math and biology. With the assistance of an HHMI-funded mini-grant, led by Karl Joplin of East Tennessee State University, and support in institutional HHMI grants at Emory and University of Delaware, these institutions held a series of summer institutes and workshops to document progress toward and address the challenges of implementing a more quantitative approach to undergraduate biology education. This report summarizes the results of the four summer institutes (2007–2010). The group developed four draft white papers, a wiki site, and a listserv. One major outcome of these meetings is this issue of CBE—Life Sciences Education, which resulted from proposals at our 2008 meeting and a January 2009 planning session. Many of the papers in this issue emerged from or were influenced by these meetings.
Welcome to this special issue of CBE—Life Sciences Education! The national scientific and academic community has issued repeated clarion calls for revising college biology curricula and the mathematical and computational preparation for future life scientists to reflect the tools and practices of science. This issue celebrates progress on incorporating quantitative reasoning into biology courses and integrating biological exemplars into mathematics courses. Within the 17 articles, seven essays, and seven features, readers find examples of innovative undergraduate research programs that emerged from research collaborations between biologists and mathematicians as well as collaborations initiated by either biologists or mathematicians. Other articles and essays illustrate collaborations between biologists and quantitative scientists that have resulted in new courses, new majors, textbooks, and modules that highlight and celebrate progress toward the BIO2010 vision.