Permutation patterns and statistics

Let S_n denote the symmetric group of all permutations of the set {1, 2, ...,n} and let S = \cup_{n\ge0} S_n. If Pi is a set of permutations, then we let Av_n(Pi) be the set of permutations in S_n which avoid every permutation of Pi in the sense of pattern avoidance. One of the celebrated notions in pattern theory is that of Wilf-equivalence, where Pi and Pi' are Wilf equivalent if #Av_n(Pi)=#Av_n(Pi') for all n\ge0. In a recent paper, Sagan and Savage proposed studying a q-analogue of this concept defined as follows. Suppose st:S->N is a permutation statistic where N represents the nonnegative integers. Consider the corresponding generating function, F_n^{st}(Pi;q) = sum_{sigma in Av_n(Pi)} q^{st sigma}, and call Pi,Pi' st-Wilf equivalent if F_n^{st}(Pi;q)=F_n^{st}(Pi';q) for all n\ge0. We present the first in-depth study of this concept for the inv and maj statistics. In particular, we determine all inv- and maj-Wilf equivalences for any Pi containd in S_3. This leads us to consider various q-analogues of the Catalan numbers, Fibonacci numbers, triangular numbers, and powers of two. Our proof techniques use lattice paths, integer partitions, and Foata's fundamental bijection. We also answer a question about Mahonian pairs raised in the Sagan-Savage article.Comment: 28 pages, 5 figures, tightened up the exposition, noted that some of the conjectures have been prove

“It’s the story”: Online Animated Simulation of Cultural Competence of Poverty -- A Pilot Study

Purpose: In this pilot study, researchers explore an online animated simulation as an educational tool for emerging health professionals to promote cultural competence of poverty, food insecurity, and the Supplemental Nutrition Assistance Program.Methods: Researchers recruited participants in the allied health sciences for focus groups to explore the effectiveness of an online animation in promoting cultural competence of poverty, food insecurity, and public assistance programs. Participants were asked about their experience with the educational tool and changes in cultural competence regarding poverty, food insecurity, and the Supplemental Nutrition Assistance Program. Participants also responded to five survey questions about their experience of the educational tool and cultural competence of poverty. Transcripts from focus groups were coded according to the five constructs of the Campinha-Bacote model for cultural competence, and further coded for recurring themes within these constructs. Results: Eleven participants across four allied health professions including nutrition, occupational therapy, nursing and pre-physical therapy participated in two focus groups. Researchers found all five constructs of the Campinha-Bacote model in analysis of focus group transcripts, with awareness and desire expressed more frequently and intensely. Participants stated the animated simulation increased their empathy for people who experience poverty, food insecurity and who need public assistance programs. Conclusion: Researchers find that this online animated simulation was an effective tool to improve cultural competence of poverty for emerging healthcare professionals. Use of similar animations by educators of healthcare professionals may also change existing negative views towards those who rely on the Supplemental Nutrition Assistance Program benefits and reduce the barrier of stigma associated with the program

Social Work Should Be More Proactive in Addressing the Need to Plan for End of Life

Few people engage in planning for life’s end and the prevalence of preparedness is particularly low in ethnic communities. As a profession, social work is well equipped to help increase planning for life’s end and the care people wish to receive. However, the profession cannot simply defer to those in hospice and palliative care settings to address this issue. There is a need for earlier and equitable access to death preparation, and social workers can be instrumental in helping to insure equal opportunities for proactive planning for death. The ways social work may become more proactive in assisting individuals and families to prepare for the end-of-life are discussed

Worship styles, musicand social identity: A communication study

This quantitative study investigates music and worship style preferences. A survey measured participants\u27 worship and music preferences in order to further examine the relationship between the two. Multiple and logistic regressions were significant indicating that preferred music genres can be used to predict one\u27s worship style preference. Further investigation used Social Identity Theory to examine the conflict that often occurs within churches over music and worship styles. Therefore, the survey included the Identification with a Psychological Group scale to measure participants\u27 identification with the Lutheran Church Missouri Synod. Multiple regression results showed a significant overall prediction of organizational identity, indicating that Missouri Synod Lutherans who prefer traditional or formal worship components identify more strongly with the larger organization, the Lutheran Church Missouri Synod (LCMS)

The Shape of LITTLE THINGS Dwarf Galaxies DDO 46 and DDO 168: Understanding the stellar and gas kinematics

We present the stellar and gas kinematics of DDO 46 and DDO 168 from the LITTLE THINGS survey and determine their respective Vmax/sigma_z,0 values. We used the KPNO's 4-meter telescope with the Echelle spectrograph as a long-slit spectrograph. We acquired spectra of DDO 168 along four position angles by placing the slit over the morphological major and minor axes and two intermediate position angles. However, due to poor weather conditions during our observing run for DDO 46, we were able to extract only one useful data point from the morphological major axis. We determined a central stellar velocity dispersion perpendicular to the disk, sigma_z,0, of 13.5+/-8 km/s for DDO 46 and of 10.7+/-2.9 km/s for DDO 168. We then derived the maximum rotation speed in both galaxies using the LITTLE THINGS HI data. We separated bulk motions from non-circular motions using a double Gaussian decomposition technique and applied a tilted-ring model to the bulk velocity field. We corrected the observed HI rotation speeds for asymmetric drift and found a maximum velocity, Vmax, of 77.4 +/- 3.7 and 67.4 +/- 4.0 km/s for DDO 46 and DDO 168, respectively. Thus, we derived a kinematic measure, Vmax/sigma_z,0, of 5.7 +/- 0.6 for DDO 46 and 6.3 +/- 0.3 for DDO 168. Comparing these values to ones determined for spiral galaxies, we find that DDO 46 and DDO 168 have Vmax/sigma_z,0 values indicative of thin disks, which is in contrast to minor-to-major axis ratio studies

Photoreceptor Inner Segment Morphology in Best Vitelliform Macular Dystrophy

PURPOSE To characterize outer retina structure in best vitelliform macular dystrophy (BVMD) and to determine the effect of macular lesions on overlying and adjacent photoreceptors. METHODS Five individuals with BVMD were followed prospectively with spectral domain optical coherence tomography and confocal and nonconfocal split-detector adaptive optics scanning light ophthalmoscopy (AOSLO). The AOSLO cone photoreceptor mosaic images were obtained within and around retinal lesions. Cone density was measured inside and outside lesions. In 2 subjects, densities were compared with published measurements acquired ∼2.5 years before. One subject was imaged 3 times over a 5-month period. RESULTS The AOSLO imaging demonstrated that photoreceptor morphology within BVMD retinal lesions was highly variable depending on the disease stage, with photoreceptor structure present even in advanced disease. The AOSLO imaging was repeatable even in severe disease over short-time and long-time intervals. Photoreceptor density was normal in retinal areas immediately adjacent to lesions and stable over ∼2.5 years. Mobile disk-like structures possibly representing subretinal macrophages were also observed. CONCLUSION Combined confocal and nonconfocal split-detector AOSLO imaging reveals substantial variability within clinical lesions in all stages of BVMD. Longitudinal cellular photoreceptor imaging could prove a powerful tool for understanding disease progression and monitoring emerging therapeutic treatment response in inherited degenerations such as BVMD

\u27Never cry for food\u27: food security, poverty, and recurring themes in news media regarding rabbit farming in East Africa

Rabbit farming is a form of low input agriculture that has potential to address food security and poverty in East Africa and beyond. For low input agriculture, farmers utilize local and affordable farm resources making it accessible across income levels. Understanding barriers and facilitators to rabbit farming could increase effectiveness of this form of low input agriculture in communities struggling with low food security and poverty, particularly for indigenous, smallholder farms. News media is an available source of data about community perceptions and practices on issues such as rabbit farming, food security, and poverty. For this qualitative study, researchers applied a priori and open coding text analysis to examine recurring themes in news media representations regarding perceptions of rabbit farming in East Africa. Results reveal that community members view rabbit farming as a community strategy that promotes better nutrition and food security while reducing poverty. Important themes included how gender and other cultural norms shaped efforts, and the role of sustainability and climate change on farming practices. Further, the easy cultivation of rabbits, funding, and protective policy and support of indigenous smallholder farms were perceived as facilitators for rabbit farming. Finally, investment in infrastructure for market, production, and knowledge-transfer of best production and business practices were considered critical to success for rabbit farmers throughout East Africa

Millisecond Pulsars: Detectable Sources of Continuous Gravitational Waves?

Laboratory searches for the detection of gravitational waves have focused on the detection of burst signals emitted during a supernova explosion, but have not resulted in any confirmed detections. An alternative approach has been to search for continuous wave (CW) gravitational radiation from the Crab pulsar. In this paper, we examine the possibility of detecting CW gravitational radiation from pulsars and show that nearby millisecond pulsars are generally much better candidates. We show that the minimum strain h_c ~ 10E-26 that can be detected by tuning an antenna to the frequency of the milli- second pulsar PSR 1957+20, with presently available detector technology, is orders of magnitude better than what has been accomplished so far by observing the Crab pulsar, and within an order of magnitude of the maximum strain that may be produced by it. In addition, we point out that there is likely to be a population of rapidly rotating neutron stars (not necessarily radio pulsars) in the solar neighborhood whose spindown evolution is driven by gravitational radiation. We argue that the projected sensitivity of modern resonant detectors is sufficient to detect the subset of this population that lies within 0.1 kpc of the sun.Comment: 17 pages (including 2 Postscript figures), LaTeX file, uses AASTeX macros, accepted for publication in the Astrophysical Journa