Faulhaber's Theorem on Power Sums

We observe that the classical Faulhaber's theorem on sums of odd powers also holds for an arbitrary arithmetic progression, namely, the odd power sums of any arithmetic progression $a+b, a+2b, ..., a+nb$ is a polynomial in $na+n(n+1)b/2$. While this assertion can be deduced from the original Fauhalber's theorem, we give an alternative formula in terms of the Bernoulli polynomials. Moreover, by utilizing the central factorial numbers as in the approach of Knuth, we derive formulas for $r$-fold sums of powers without resorting to the notion of $r$-reflexive functions. We also provide formulas for the $r$-fold alternating sums of powers in terms of Euler polynomials.Comment: 12 pages, revised version, to appear in Discrete Mathematic

CHANGING AN ONLINE VIDEO MEETING BACKGROUND IN REAL-TIME USING DEEP LEARNING

This proposal provides a technique to change an online video meeting background in real-time using deep learning. By changing the background video for participants of a meeting, the participants can protect their accuracy. The background-changing technique of this proposal may include a deep learning model for video semantic segmentation. One or more Spatio-Temporal Transformer Gated Recurrent Units (STGRUs) may be utilized to enhance classification accuracy and to add an optical flow into the model; thereby increasing calculation speed

HIV drug resistance, tropism, and genetic diversity in Black men who have sex with men

Black men who have sex with men (MSM) are disproportionately affected by HIV in the United States (US). Despite representing less than 1% of the US population, Black MSM accounted for the highest number of new HIV diagnoses in 2014. Culturally-tailored interventions are needed to control the HIV epidemic in this population. The HIV Prevention Trials Network (HPTN) 061 study was designed to assess the feasibility of a multi-component intervention for reducing HIV incidence among Black MSM. The HPTN 061 study enrolled 348 HIV-infected men and 1,205 HIV-uninfected men; 28 men seroconverted during the study for an annual incidence rate of 3.0% overall and 5.9% among younger men (aged 18-30 years). Men in the HPTN 061 study completed detailed demographic and behavioral assessments at each study visit, which included an evaluation of risk behaviors associated with HIV transmission and acquisition. Demographic and behavioral factors that influence HIV transmission and acquisition may also impact the characteristics of infecting viral populations and their subsequent evolution. The work in this dissertation analyzed factors associated with HIV drug resistance, tropism, and genetic diversity in this cohort of Black MSM in the US. These findings provided new insights relevant to HIV treatment and prevention in this high-risk population

A magnetic resonance approach to neurodegeneration

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Nuclear Engineering, 1997.Includes bibliographical references.by Yin-Ching Iris Chen.Ph.D

Towards the Design of a Smartphone-Based Biofeedback Breathing Training: Indentifying Diaphragmatic Breathing Patterns From a Smartphones\u27 Microphone

Asthma, diabetes, hypertension, or major depression are non-communicable diseases (NCDs) and impose a major burden on global health. Stress is linked to both the causes and consequences of NCDs and it has been shown that biofeedback-based breathing trainings (BBTs) are effective in coping with stress. Here, diaphragmatic breathing, i.e. deep abdominal breathing, belongs to the most distinguished breathing techniques. However, high costs and low scalability of state-of-the-art BBTs that require expensive medical hardware and health professionals, represent a significant barrier for their widespread adoption. Health information technology has the potential to address this important practical problem. Particularly, it has been shown that a smartphone microphone has the ability to record audio signals from exhalation in a quality that can be compared to professional respiratory devices. As this finding is highly relevant for low-cost and scalable smartphone-based BBTs (SBBT) and – to the best of our knowledge - because it has not been investigated so far, we aim to design and evaluate the efficacy of such a SBBT. As a very first step, we apply design-science research and investigate in this research-in-progress the relationship of diaphragmatic breathing and its acoustic components by just using a smartphone’s microphone. For that purpose, we review related work and develop our hypotheses based on justificatory knowledge from physiology, physics and acoustics. We finally describe a laboratory study that is used to test our hypotheses. We conclude with a brief outlook on future work