Taylor's Theorem for Functionals on BMO with Application to BMO Local Minimizers

In this note two results are established for energy functionals that are given by the integral of $W(\mathbf x,\nabla \mathbf u(\mathbf x))$ over $\Omega \subset\mathbb{R}^n$ with $\nabla \mathbf u \in BMO(\Omega;{\mathbb R}^{N\times n})$, the space of functions of Bounded Mean Oscillation of John & Nirenberg. A version of Taylor's theorem is first shown to be valid provided the integrand $W$ has polynomial growth. This result is then used to demonstrate that, for the Dirichlet, Neumann, and mixed problems, every Lipschitz-continuous solution of the corresponding Euler-Lagrange equations at which the second variation of the energy is uniformly positive is a strict local minimizer of the energy in $W^{1,BMO}(\Omega;\mathbb{R}^N)$, the subspace of the Sobolev space $W^{1,1}(\Omega;\mathbb{R}^N)$ for which the weak derivative $\nabla\mathbf u \in BMO(\Omega;{\mathbb R}^{N\times n})$.Comment: 8 page

LpL^p-Taylor approximations characterize the Sobolev space W1,pW^{1,p}

In this note, we introduce a variant of Calder\'on and Zygmund's notion of $L^p$-differentiability - an \emph{$L^p$-Taylor approximation}. Our first result is that functions in the Sobolev space $W^{1,p}(\mathbb{R}^N)$ possess a first order $L^p$-Taylor approximation. This is in analogy with Calder\'on and Zygmund's result concerning the $L^p$-differentiability of Sobolev functions. In fact, the main result we announce here is that the first order $L^p$-Taylor approximation characterizes the Sobolev space $W^{1,p}(\mathbb{R}^N)$, and therefore implies $L^p$-differentiability. Our approach establishes connections between some characterizations of Sobolev spaces due to Swanson using Calder\'on-Zygmund classes with others due to Bourgain, Brezis, and Mironescu using nonlocal functionals with still others of the author and Mengesha using nonlocal gradients. That any two characterizations of Sobolev spaces are related is not surprising, however, one consequence of our analysis is a simple condition for determining whether a function of bounded variation is in a Sobolev space.Comment: 7 pages. Preprint of an article to appear in Comptes Rendus - the exposition of the two articles is substantially different and the full article will not be available as an arxiv paper. The title and abstract displaying on arxiv have been changed to that of the article in its more polished for

The fractional variation and the precise representative of BVα,pBV^{\alpha,p} functions

We continue the study of the fractional variation following the distributional approach developed in the previous works arXiv:1809.08575, arXiv:1910.13419 and arXiv:2011.03928. We provide a general analysis of the distributional space $BV^{\alpha,p}(\mathbb{R}^n)$ of $L^p$ functions, with $p\in[1,+\infty]$, possessing finite fractional variation of order $\alpha\in(0,1)$. Our two main results deal with the absolute continuity property of the fractional variation with respect to the Hausdorff measure and the existence of the precise representative of a $BV^{\alpha,p}$ function.Comment: 32 page

Does drug‐induced sleep endoscopy predict surgical success in transoral robotic multilevel surgery in obstructive sleep apnea?

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/136419/1/lary26255_am.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/136419/2/lary26255.pd

Microstructural Changes in Human Ingestive Behavior After Roux-en-Y Gastric Bypass During Liquid Meals

BACKGROUND. Roux-en-Y gastric bypass (RYGB) decreases energy intake and is, therefore, an effective treatment of obesity. The behavioral bases of the decreased calorie intake remain to be elucidated. We applied the methodology of microstructural analysis of meal intake to establish the behavioral features of ingestion in an effort to discern the various controls of feeding as a function of RYGB. METHODS. The ingestive microstructure of a standardized liquid meal in a cohort of 11 RYGB patients, in 10 patients with obesity, and in 10 healthy-weight adults was prospectively assessed from baseline to 1 year with a custom-designed drinkometer. Statistics were performed on log-transformed ratios of change from baseline so that each participant served as their own control, and proportional increases and decreases were numerically symmetrical. Data-driven (3 seconds) and additional burst pause criteria (1 and 5 seconds) were used. RESULTS. At baseline, the mean meal size (909.2 versus 557.6 kCal), burst size (28.8 versus 17.6 mL), and meal duration (433 versus 381 seconds) differed between RYGB patients and healthy-weight controls, whereas suck volume (5.2 versus 4.6 mL) and number of bursts (19.7 versus 20.1) were comparable. At 1 year, the ingestive differences between the RYGB and healthy-weight groups disappeared due to significantly decreased burst size (P = 0.008) and meal duration (P = 0.034) after RYGB. The first-minute intake also decreased after RYGB (P = 0.022). CONCLUSION. RYGB induced dynamic changes in ingestive behavior over the first postoperative year. While the eating pattern of controls remained stable, RYGB patients reduced their meal size by decreasing burst size and meal duration, suggesting that increased postingestive sensibility may mediate postbariatric ingestive behavior. TRIAL REGISTRATION. NCT03747445; https://clinicaltrials.gov/ct2/show/NCT03747445. FUNDING. This work was supported by the University of Zurich, the Swiss National Fund (32003B_182309), and the Olga Mayenfisch Foundation. Bálint File was supported by the Hungarian Brain Research Program Grant (grant no. 2017-1.2.1-NKP-2017-00002)

COVID- 19 pandemic and health care disparities in head and neck cancer: Scanning the horizon

The COVID- 19 pandemic has profoundly disrupted head and neck cancer (HNC) care delivery in ways that will likely persist long term. As we scan the horizon, this crisis has the potential to amplify preexisting racial/ethnic disparities for patients with HNC. Potential drivers of disparate HNC survival resulting from the pandemic include (a) differential access to telemedicine, timely diagnosis, and treatment; (b) implicit bias in initiatives to triage, prioritize, and schedule HNC- directed therapy; and (c) the marked changes in employment, health insurance, and dependent care. We present four strategies to mitigate these disparities: (a) collect detailed data on access to care by race/ethnicity, income, education, and community; (b) raise awareness of HNC disparities; (c) engage stakeholders in developing culturally appropriate solutions; and (d) ensure that surgical prioritization protocols minimize risk of racial/ethnic bias. Collectively, these measures address social determinants of health and the moral imperative to provide equitable, high- quality HNC care.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/156210/2/hed26345.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/156210/1/hed26345_am.pd

Weekly chemotherapy with radiation versus high‐dose cisplatin with radiation as organ preservation for patients with HPV‐positive and HPV‐negative locally advanced squamous cell carcinoma of the oropharynx

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/106948/1/hed23339.pd

Attitudes and Performance: An Analysis of Russian Workers

This paper investigates the relationship between locus of control and performance among Russian employees, using survey data collected at 28 workplaces in 2002 in Taganrog and at 47 workplaces in 2003 in Ekaterinburg. We develop a measure that allows us to categorize the Russian employees participating in our survey as exhibiting an internal or external locus of control. We then assess the extent to which there are significant differences between “internals” and “externals” in work-related attitudes that may affect performance. In particular, we focus on (1) attitudes about outcomes associated with hard work, (2) level of job satisfaction, (3) expectation of receiving a desired reward, and (4) loyalty to and involvement with one’s organization. In each case we identify where gender and generational differences emerge. Our main objective is to determine whether Russian employees who exhibit an internal locus of control perform better than employees with an external locus of control. Our performance measures include earnings, expected promotions, and assessments of the quantity and quality of work in comparison to others at the same organization doing a similar job. Controlling for a variety of worker characteristics, we find that (1) individuals who exhibit an internal locus of control perform better, but this result is not always statistically significant; (2) even among “internals,” women earn significantly less than men and have a much lower expectation of promotion; (3) even among “internals,” experience with unemployment has a negative influence on performance.http://deepblue.lib.umich.edu/bitstream/2027.42/40144/3/wp758.pd