Proof of Koml\'os's conjecture on Hamiltonian subsets

Koml\'os conjectured in 1981 that among all graphs with minimum degree at least $d$, the complete graph $K_{d+1}$ minimises the number of Hamiltonian subsets, where a subset of vertices is Hamiltonian if it contains a spanning cycle. We prove this conjecture when $d$ is sufficiently large. In fact we prove a stronger result: for large $d$, any graph $G$ with average degree at least $d$ contains almost twice as many Hamiltonian subsets as $K_{d+1}$, unless $G$ is isomorphic to $K_{d+1}$ or a certain other graph which we specify.Comment: 33 pages, to appear in Proceedings of the London Mathematical Societ

Assessing the performance of the Asian/Pacific islander identification algorithm to infer Hmong ethnicity from electronic health records in California.

OBJECTIVE:This study assesses the performance of the North American Association of Central Cancer Registries Asian/Pacific Islander Identification Algorithm (NAPIIA) to infer Hmong ethnicity. DESIGN AND SETTING:Analyses of electronic health records (EHRs) from 1 January 2011 to 1 October 2015. The NAPIIA was applied to the EHR data, and self-reported Hmong ethnicity from a questionnaire was used as the gold standard. Sensitivity, specificity, positive (PPV) and negative predictive values (NPVs) were calculated comparing the source data ethnicity inferred by the algorithm with the self-reported ethnicity from the questionnaire. PARTICIPANTS:EHRs indicating Hmong, Chinese, Vietnamese and Korean ethnicity who met the original study inclusion criteria were analysed. RESULTS:The NAPIIA had a sensitivity of 78%, a specificity of 99.9%, a PPV of 96% and an NPV of 99%. The prevalence of Hmong population in the sample was 3.9%. CONCLUSION:The high sensitivity of the NAPIIA indicates its effectiveness in detecting Hmong ethnicity. The applicability of the NAPIIA to a multitude of Asian subgroups can advance Asian health disparity research by enabling researchers to disaggregate Asian data and unmask health challenges of different Asian subgroups

Colorectal Cancer Brochure Development for African Americans

Introduction: African Americans are more likely to die from colorectal cancer (CRC) than any other racial/ethnic group in the United States. Unfortunately, African Americans are also less likely to undergo screening for CRC than their White counterparts. Focus groups methodology was used to refine educational brochures designed to increase CRC screening among African Americans. Methods: Two series of focus groups were completed, with a total of seven groups and 39 participants. Six different brochures (stage-matched and culturally sensitive) designed to promote CRC screening among African Americans were evaluated. Results: All participants thought that the brochures motivated them to talk with their health care providers about screening. Cost, pain, medical mistrust and fear were identified as major barriers and the brochures were modified to address these concerns. Conclusions: Focus groups methodology with African Americans can be used to inform brochures designed to increase African Americans CRC screening that addresses their major concerns

Technology and Caregiving: Emerging Interventions and Directions for Research.

An array of technology-based interventions has increasingly become available to support family caregivers, primarily focusing on health and well-being, social isolation, financial, and psychological support. More recently the emergence of new technologies such as mobile and cloud, robotics, connected sensors, virtual/augmented/mixed reality, voice, and the evermore ubiquitous tools supported by advanced data analytics, coupled with the integration of multiple technologies through platform solutions, have opened a new era of technology-enabled interventions that can empower and support family caregivers. This paper proposes a conceptual framework for identifying and addressing the challenges that may need to be overcome to effectively apply technology-enabled solutions for family caregivers. The paper identifies a number of challenges that either moderate or mediate the full use of technologies for the benefit of caregivers. The challenges include issues related to equity, inclusion, and access; ethical concerns related to privacy and security; political and regulatory factors affecting interoperability and lack of standards; inclusive/human-centric design and issues; and inherent economic and distribution channel difficulties. The paper concludes with a summary of research questions and issues that form a framework for global research priorities

A relative of Hadwiger's conjecture

Hadwiger's conjecture asserts that if a simple graph $G$ has no $K_{t+1}$ minor, then its vertex set $V(G)$ can be partitioned into $t$ stable sets. This is still open, but we prove under the same hypotheses that $V(G)$ can be partitioned into $t$ sets $X_1,\ldots, X_t$, such that for $1\le i\le t$, the subgraph induced on $X_i$ has maximum degree at most a function of $t$. This is sharp, in that the conclusion becomes false if we ask for a partition into $t-1$ sets with the same property.Comment: 6 page

Are providers prepared for genomic medicine: interpretation of Direct-to-Consumer genetic testing (DTC-GT) results and genetic self-efficacy by medical professionals.

BACKGROUND:Precision medicine is set to deliver a rich new data set of genomic information. However, the number of certified specialists in the United States is small, with only 4244 genetic counselors and 1302 clinical geneticists. We conducted a national survey of 264 medical professionals to evaluate how they interpret genetic test results, determine their confidence and self-efficacy of interpreting genetic test results with patients, and capture their opinions and experiences with direct-to-consumer genetic tests (DTC-GT). METHODS:Participants were grouped into two categories, genetic specialists (genetic counselors and clinical geneticists) and medical providers (primary care, internists, physicians assistants, advanced nurse practitioners, etc.). The survey (full instrument can be found in the Additional file 1) presented three genetic test report scenarios for interpretation: a genetic risk for diabetes, genomic sequencing for symptoms report implicating a potential HMN7B: distal hereditary motor neuropathy VIIB diagnosis, and a statin-induced myopathy risk. Participants were also asked about their opinions on DTC-GT results and rank their own perceived level of preparedness to review genetic test results with patients. RESULTS:The rates of correctly interpreting results were relatively high (74.4% for the providers compared to the specialist's 83.4%) and age, prior genetic test consultation experience, and level of trust assigned to the reports were associated with higher correct interpretation rates. The self-selected efficacy and the level of preparedness to consult on a patient's genetic results were higher for the specialists than the provider group. CONCLUSION:Specialists remain the best group to assist patients with DTC-GT, however, primary care providers may still provide accurate interpretation of test results when specialists are unavailable