Constructing graphs with no immersion of large complete graphs

In 1989, Lescure and Meyniel proved, for $d=5, 6$, that every $d$-chromatic graph contains an immersion of $K_d$, and in 2003 Abu-Khzam and Langston conjectured that this holds for all $d$. In 2010, DeVos, Kawarabayashi, Mohar, and Okamura proved this conjecture for $d = 7$. In each proof, the $d$-chromatic assumption was not fully utilized, as the proofs only use the fact that a $d$-critical graph has minimum degree at least $d - 1$. DeVos, Dvo\v{r}\'ak, Fox, McDonald, Mohar, and Scheide show the stronger conjecture that a graph with minimum degree $d-1$ has an immersion of $K_d$ fails for $d=10$ and $d\geq 12$ with a finite number of examples for each value of $d$, and small chromatic number relative to $d$, but it is shown that a minimum degree of $200d$ does guarantee an immersion of $K_d$. In this paper we show that the stronger conjecture is false for $d=8,9,11$ and give infinite families of examples with minimum degree $d-1$ and chromatic number $d-3$ or $d-2$ that do not contain an immersion of $K_d$. Our examples can be up to $(d-2)$-edge-connected. We show, using Haj\'os' Construction, that there is an infinite class of non-$(d-1)$-colorable graphs that contain an immersion of $K_d$. We conclude with some open questions, and the conjecture that a graph $G$ with minimum degree $d - 1$ and more than $\frac{|V(G)|}{1+m(d+1)}$ vertices of degree at least $md$ has an immersion of $K_d$

Distribution and Properties of the Critical Values of Random Polynomials With Non-Independent and Non-Identically Distributed Roots

This paper considers the pairing between the distribution of the roots and the distribution of the critical values of random polynomials.  The primary model of random polynomial considered in this paper consists of monic polynomials of degree n with a single complex variable z where the roots of the random polynomial are complex valued random variables that are chosen from two independent sequences of iid, complex valued random variables.  The distribution of the random variables from each of the two sequences are different, producing roots of the random polynomial which have non-identical distributions.  Furthermore, both the iid, complex valued random variables from one of the sequences of random variables and the complex conjugates of those random variables are roots of the random polynomial.  Hence, this model of monic random polynomials of degree n has roots that are random variables which are not independent, due to the dependence based on complex conjugates, and the non-identical distributions which arise from the use of the two independent sequences.  This paper also describes the relationship between the roots and critical values of monic random polynomials of degree n where the roots are chosen to be random variables and their complex conjugates where the random variables are from a sequence of iid complex valued random variables

A Comparison of Treatment Options for Carpal Boss: A Critically Appraised Topic

Context: Carpal bossing is a bony growth or mass that typically occurs at the 2nd or 3rd carpometacarpal joint. Carpal bossing is often overlooked placing the patient at an increased risk for pain or injury, such as osteoarthritis or inflammatory joint disease if left untreated. Individuals such as combat sport athletes who experience repetitive trauma to this area are at a high risk to develop carpal bossing. The literature suggests conservative or surgical interventions to manage symptoms. The goal of this systematic review is to synthesize the current literature for clinical knowledge and intervention outcomes for carpal bossing. Methods: A systematic search of the literature was performed across 3 electronic databases (Science Direct, PubMed, and EBSCOhost) to identify articles that investigated the effects of surgical intervention or conservative management for carpal bossing. A combination of the keywords and Boolean operators (Carpal Bossing, Carpal Boss, Surgical Intervention, Wedge Resection, Excision, Conservative Treatment, and Intervention) related to the research question were used. The search was restricted to full text, human studies (including cadaveric studies) research, and manuscripts available in English. Articles were included if they examined the effect of either conservative or surgical interventions for the treatment of carpal bossing. Articles were excluded from the review if the study did not examine carpal bossing treatment options or did not include pain, range of motion, strength, or functional measures of the hand and wrist. Two independent reviewers used the Joanna Briggs Institute Checklist for Case Reports and the Checklist for Case Studies to appraise the quality of the articles. A score of 50% was used to remove low-quality studies. The Strength of Recommendation Taxonomy (SORT) method was used to grade the evidence for the articles included. Results: After the initial search, 10 articles met the inclusion criteria, while 3 were eliminated due to low quality appraisal scores. The average scores for case reports and case studies were 5.5/7 or 7.5/9 respectively. There was a total of 58 participants across the 7 studies. Generally speaking, conservative treatment reduced average daily pain and patients were able to return to full participation within 2 weeks. Conversely, patients undergoing surgical intervention experienced episodic pain, including over the surgical incision, typically averaging 2/10 on the visual analog scale. Findings from the surgical intervention showed inconsistent measurements for wrist/hand strength and range of motion. There is level C evidence on the treatment for carpal bossing. Conclusion: The limited evidence suggests conservative management may reduce pain and improve clinical outcomes. However, clinicians should consider the level C evidence with skepticism as the quality of evidence on this topic is low. Further investigations should be performed with more rigor

Losing Sight of Ourselves: A Theoretical Analysis of Reality Television in the United States

The focus of this research is the emergence and encouragement of the false self in our society and how this is portrayed through four reality television shows: Toddlers and Tiaras, Hoarders, Sister Wives and Catfish: The TV Show. Content analysis in combination with various theoretical perspectives will be utilized in order to examine the effects of narcissism, consumerism and the emergence of the false self. The limitless character of a consumer society coupled with narcissism and an increased focus on the self contributes to the development of the false self within the individual. People may not even be aware of the push to be narcissistic, focused on our own biographies and self-promotion, yet people are aware of their suffering and unhappiness. Many individuals are left questioning why it is that they are never completely satisfied even as they accumulate notoriety, success, material wealth and possessions. An ideology of greatness and being the best is found in so many avenues of our daily lives, and at times it can be overwhelming, and if we do not possess these skills and qualities we are encouraged to just fake it

How safe and effective is ondansetron for nausea and vomiting in pregnancy?

Q: How safe and effective is ondansetron for nausea and vomiting in pregnancy? Evidence-based answer: oral ondansetron is more effective than a combination of pyridoxine and doxylamine for outpatient treatment of nausea and vomiting in pregnancy (strength of recommendation [SOR]: B, randomized controlled trial [RCT]). For moderate to severe nausea and vomiting, intravenous (IV) ondansetron is at least as effective as IV metoclopramide and may cause fewer adverse reactions (SOR: B, RCTs). Disease registry, case-control, and cohort studies report a slight increase in the risk of cardiac defects with ondansetron use in first-trimester pregnancies, but no major or other birth defects are associated with ondansetron exposure (SOR: B, a systematic review of observational trials and a single retrospective cohort study). A specialty society guideline recommends weighing the risks and benefits of ondansetron use before 10 weeks' gestational age and suggests reserving ondansetron for patients who have persistent nausea and vomiting unresponsive to first- and second-line treatments (SOR: C, expert opinion).Kimberly L. Collins, MD; Megan Wilson, MD; E. Chris Vincent, MD, University of Washington, Seattle ; Sarah Safranek, MLIS, University of Washington, SeattleIncludes bibliographical reference

Misplaced Trust: Measuring the Interference of Machine Learning in Human Decision-Making

ML decision-aid systems are increasingly common on the web, but their successful integration relies on people trusting them appropriately: they should use the system to fill in gaps in their ability, but recognize signals that the system might be incorrect. We measured how people's trust in ML recommendations differs by expertise and with more system information through a task-based study of 175 adults. We used two tasks that are difficult for humans: comparing large crowd sizes and identifying similar-looking animals. Our results provide three key insights: (1) People trust incorrect ML recommendations for tasks that they perform correctly the majority of the time, even if they have high prior knowledge about ML or are given information indicating the system is not confident in its prediction; (2) Four different types of system information all increased people's trust in recommendations; and (3) Math and logic skills may be as important as ML for decision-makers working with ML recommendations.Comment: 10 page