Geometric combinatorial algebras: cyclohedron and simplex

In this paper we report on results of our investigation into the algebraic structure supported by the combinatorial geometry of the cyclohedron. Our new graded algebra structures lie between two well known Hopf algebras: the Malvenuto-Reutenauer algebra of permutations and the Loday-Ronco algebra of binary trees. Connecting algebra maps arise from a new generalization of the Tonks projection from the permutohedron to the associahedron, which we discover via the viewpoint of the graph associahedra of Carr and Devadoss. At the same time that viewpoint allows exciting geometrical insights into the multiplicative structure of the algebras involved. Extending the Tonks projection also reveals a new graded algebra structure on the simplices. Finally this latter is extended to a new graded Hopf algebra (one-sided) with basis all the faces of the simplices.Comment: 23 figures, new expanded section about Hopf algebra of simplices, with journal correction

Stress fracture of bilateral tibial metaphysis due to ceremonial march training: a case report

Stress fractures are caused by repetitive microtraumas that occur during unusual or increased activities. Clinical suspicion is essential for the diagnosis. A twenty-years old soldier was presented with bilateral knee pain and restriction of knee movements after a period of training for ceremonial march. Although plain X-rays were normal, scintigraphy and MRI revealed stress fractures at metaphyseal region of both tibias. History of a patient presenting with persisting joint or bone pain after an unusual repetitive activity should be delicately inquired. Typical history, although pain might be localized to unusual sites, should raise the suspicion of a stress fracture

International Perspectives on Nonformal Education

The New England Regional Meeting of the Comparative and International Education Society was held on the campus of the University of Massachusetts, Amherst, on 3 May, 1979. The conference was co-sponsored by the Division of Community Education, Springfield College, and the Center for International Education, School of Education, University of Massachusetts. The theme of the conference was International Perspectives on Nonformal Education. The papers delivered ranged in topics from the use of traditional art forms and poetry as a medium of nonformal education to the discussion of the philosophical foundations underlying the field. Case studies of specific nonformal education projects helped to highlight the conference. A total fifteen papers were delivered, all of which are included in their original form in this document. The papers represent the views of the authors and not necessarily those of the organizers

Measures of racial/ethnic health disparities in cancer mortality rates and the influence of socioeconomic status.

OBJECTIVES: In the 1990s, U.S. cancer mortality rates declined due to reductions in tobacco use among men and beneficial cancer interventions, such as mammography and Pap smears. We examined the cancer rates by racial/ethnic group, socioeconomic status and time period to identify disparities underlying the overall mortality trend. METHODS: We examined racial/ethnic disparities by measuring excess cancer burden [rate ratio (RR) and ratio differences (RD)] and trends in their cancer rates for nine cancer sites. The trend (T) is calculated as a ratio of the average annual cancer mortality rate for 1995-2000 relative to the rate for 1990-1994 for three levels of poverty (counties with <10% living below the poverty level, 10% - <20% and > or =20%) for the major racial/ethnic populations. We also compared the trend for each racial/ethnic SES group to the trend for lowest SES white group (TD). RESULTS: Blacks have RR disparities relative to whites for each cancer site examined, except for female lung cancer, while the other minorities had RR disparities for cervical cancer (RR>1). There are increases in RR disparities from 1990-1994 to 1995-2000 (RD>0) for colorectal cancer, prostate cancer and breast cancer for each racial/ethnic minority. Whites and blacks had declining trends for every SES group (T<1) and positive high SES gradients (the highest SES group had the best trend and the lowest SES group had the worst trend) at each cancer site, except female lung cancer (T>1). In contrast, American Indians/Alaska natives, Hispanics and Asians/ Pacific Islanders had increasing trends for some of their cancer sites, and their trends did not have the SES gradients. CONCLUSIONS: Increases in racial/ethnic disparities (RD>0) for colorectal, breast and prostate cancer were largest in the lowest SES groups. At some cancer sites, the highest SES group for minorities had worse trend results than the trends for the lowest SES white group (TD>0)

Activism In the Digital Age: The Link Betwee Social Media Engagement With Black Lives Matter-Relevant Content and Mental Health

Study Objectives:: This study aimed to estimate the 12-month prevalence of diagnosed sleep disorders among veterans with and without serious mental illnesses (SMI) in VA health record data in 2019. We also examined diagnosed sleep disorders across a 9-year period and explored associations with demographic and health factors. Methods:: This study used health record data from VISN 4 of the Veterans Health Administration (VHA) from 2011-2019. SMI diagnoses included schizophrenia and bipolar spectrum diagnoses as well as major depression with psychosis. Sleep diagnoses included insomnias, hypersomnias, sleep-related breathing disorders, circadian rhythm sleep-wake disorders, and sleep-related movement disorders. Demographic and health-related factors were also collected from the record. Results:: In 2019, 21.8% of veterans with SMI were diagnosed with a sleep disorder. This is a significantly higher proportion than for veterans without SMI, 15.1% of whom were diagnosed with a sleep disorder. Sleep disorder rates were highest in veterans with a chart diagnosis of major depression with psychosis. From 2011 to 2019, the overall prevalence of sleep disorders in veterans with SMI more than doubled (10.2% to 21.8%), suggesting improvements in the detection and diagnosis of sleep concerns for this group. Conclusions:: Our findings suggest that identification and diagnosis of sleep disorders for veterans with SMI has improved over the past decade, though diagnoses still likely underrepresent actual prevalence of clinically relevant sleep concerns. Sleep concerns may be at particularly high risk of going untreated in veterans with schizophrenia-spectrum disorders

Osteoid osteoma: percutaneous radio-frequency ablation

To evaluate a percutaneous technique for in situ destruction of osteoid osteoma. Radio-frequency ablation was performed in 18 patients with osteoid osteoma (17 male, one female; age range, 8-42 years). Diagnosis was established by means of clinical and radiographic features and confirmed by means of needle biopsy findings. No attempt was made to remove the lesion. A small radio-frequency electrode introduced into the lesion through the biopsy track was used to produce thermal necrosis of a 1-cm sphere of tissue. Symptoms were completely relieved in 16 (89%) of 18 patients. In one patient, a second procedure was required for pain relief. All but two patients underwent treatment as outpatients: These two were hospitalized for 1 night only. All patients resumed normal daily activities immediately. No casts or external supports were required; there were no complications. Twelve patients were followed up for more than 1 year. There were no recurrences Radio-frequency ablation of osteoid osteoma is a promising alternative to surgery in selected patients

Relationships between Sleep Quality, Introspective Accuracy, and Confidence Differ among People with Schizophrenia, Schizoaffective Disorder, and Bipolar Disorder with Psychotic Features

People with schizophrenia-spectrum and bipolar disorders have difficulty accurately estimating their abilities and skills (impaired introspective accuracy [IA]) and tend to over- or underestimate their performance. This discrepancy between self-reported and objective task performance has been identified as a significant predictor of functional impairment. Yet, the factors driving this discrepancy are currently unclear. To date, the relationships between sleep quality and IA have not been examined. The current study aimed to explore the relationships between sleep quality and IA in participants diagnosed with schizophrenia (SCZ; n = 36), schizoaffective disorder (SCZ-A; n = 55), and bipolar disorder with psychotic features (BP; n = 87). Participants completed tasks of emotion recognition, estimated their performance on the tasks (used to calculate IA), and provided confidence ratings for their accuracy judgments. Participants also self-reported their sleep quality. These results suggest significantly greater discrepancies between self-reported and actual task scores for those with SCZ and SCZ-A compared to participants with BP. For those with SCZ, lower confidence on the tasks and underestimation of abilities were associated with lower sleep quality, while for those with SCZ-A, lower sleep quality was associated with higher confidence and overestimation of performance. Results suggest differential relationships between diagnostic groups. Future research is needed to further explore the factors driving these differing relationships, particularly the contrasting relationships between SCZ and SCZ-A