Circumference and Pathwidth of Highly Connected Graphs

Birmele [J. Graph Theory, 2003] proved that every graph with circumference t has treewidth at most t-1. Under the additional assumption of 2-connectivity, such graphs have bounded pathwidth, which is a qualitatively stronger result. Birmele's theorem was extended by Birmele, Bondy and Reed [Combinatorica, 2007] who showed that every graph without k disjoint cycles of length at least t has bounded treewidth (as a function of k and t). Our main result states that, under the additional assumption of (k + 1)- connectivity, such graphs have bounded pathwidth. In fact, they have pathwidth O(t^3 + tk^2). Moreover, examples show that (k + 1)-connectivity is required for bounded pathwidth to hold. These results suggest the following general question: for which values of k and graphs H does every k-connected H-minor-free graph have bounded pathwidth? We discuss this question and provide a few observations.Comment: 11 pages, 4 figure

Trying to stay (not test) positive.

https://scholarship.rollins.edu/six-word_memoirs/1025/thumbnail.jp

A Man’s World? Analysing gender diversity within London’s West End Pit Orchestras

The Musicians’ Union conducted an informal survey in 2018 and concluded that only 11% of the musicians working within the West End pit orchestras were female and in 2023 celebrated that this had increased to 27% (Musicians’ Union, 2018; Musicians’ Union 2023). However, the statistics are informal and unvalidated, and do not reflect a gender diverse workforce. As a young, female musician aspiring to work in the pit orchestras, it quickly became apparent that the industry was dominated by men. This sparked a drive to research and investigate if my perception was in fact true – that the West End was a Man’s World. This research project uses a combined methodology of statistical analysis and ethnography through an online survey and semi-structured interviews. Statistics were gathered through archival research and collection of data from a range of historical programmes. The online survey engaged with a wide range of musicians currently working in the musical theatre industry, and further interviews were undertaken with nine musicians and Musical Directors. The survey responses and interviews provided insight into the perceptions of those actively working within the pit orchestras, the ‘men’s club’ culture, the lack of role models and issues within the education system. Key themes are drawn together and conclude that the factors affecting gender diversity are complex and multi-faceted

“You Can Be Anything You Want : An Analysis of Gender Roles in Early Childhood Literature

The theme of gender roles is something that shows up in every work of literature. In early children’s literature, the vast majority of these stories portray the most common gender stereotypes, such as girls wearing pink and playing with dolls, while boys are wearing blue and playing with cars and trucks. The families’ roles are also seen in these books. For example, the mother figure is usually seen staying at home with the children and working in the kitchen or outside in the garden, while the father is often portrayed coming home from a long day of work in a suit and tie. These gender roles are often portrayed in similar ways throughout preschool and kindergarten literature. This is a critical period to establish self-concept and gender roles. Therefore, it is important to examine how gender roles are described in the children’s books (ages 3 to 6 years). I will collect data (children’s books ages 3 to 6 years) from the Theodor Seuss Geisel Award winners and honorees located in either Murray State University\u27s Waterfield Library or the Murray State University Curriculum Materials Center and analyze the collected data using the constant comparative method. Qualitative data regarding the various themes found in the literature will be analyzed as well as the quantitative data regarding the number of times each theme is found in the books

Epigenetic silencing of SOCS3 expression contributes to fibrosis in Crohn’s disease

Identified risk polymorphisms affecting the Jak-STAT3 pathway in patients with Crohn’s disease could affect TGF-β1 and collagen I expression and in the pathway’s negative regulator, SOCS3. Genetic factors, however, account for only ~25% of disease. Epigenetic events also shape gene expression. Recent experiments showed that autocrine IL-6 production in mesenchymal cells, subepithelial myofibroblasts (SEMF) and muscle cells, of patients with fibrostenotic Crohn’s disease causes sustained Jak-STAT3 activity, excess TGF-β1 and Collagen I production and fibrosis. SOCS3 paradoxically decreased in these cells. We now identify epigenetic mechanisms that silence SOCS3 expression in SEMF of patients with fibrostenotic Crohn’s disease. In a previous experiment, using isolated SEMF of normal ileum and affected ileum from patients with each Crohn’s phenotype, inflammatory (Montreal B1), fibrostenotic (B2) and penetrating (B3), we confirmed decreased SOCS3 protein levels were unique to B2 patients. Expression of miR-19b increased in SEMF of affected ileum. SOCS3 transcriptional activity decreased after transfection of miR-19b mimic and increased when antagomiR-19b was expressed. Epigenetic silencing of SOCS3 in ileal SEMF of patients with fibrostenotic Crohn’s disease occurs by increased miR-19b mediated inhibition of SOCS3

Neurological approach measuring attentional variations among children with high-functioning autism spectrum disorder, sensory processing difficulties and age-matched peers, A

2015 Spring.Includes bibliographical references.Children with high functioning autism (HFA) and children with sensory processing difficulties (SPD) can have challenges processing auditory stimuli, which may contribute to difficulties with performance of everyday tasks. Few studies assess relationships between neurological measures with behavioral attention measures, yet the benefits of doing so are invaluable in understanding the brain and behavior connections in children who have difficulties processing sensory information. Therefore, this study focuses on examining the impact of neurological auditory processing on performance on tasks that require attention among children with HFA, SPD and typically developing (TD) controls. Participants included 20 children with HFA (mean age = 8.94 ± 2.03 years), 9 children with SPD (mean age = 6.57 ± 1.26 years), and 22 TD gender and age-matched peers (mean age = 8.46 ± 2.39 years). Groups were compared according to behavioral assessment of everyday task performance and a neurological paradigm. The Test of Everyday Attention for Children (TEA-Ch) evaluates a child's attention during tasks that correspond with three subtypes of attention, while the orientation and habituation electroencephalography (EEG) paradigm allows for sensory gating and habituation neural processing measurement and analysis. Based on the TEA-Ch scores, children in with HFA and SPD groups had significant differences with attention demands, especially in the domains of control/shift and sustained attention, when compared to the TD group. On the neurological measures, children with HFA displayed similar sensory gating abilities as compared to TD peers, including a reduction of both N1 and N2 amplitudes from tone 1 to tone 2, while children with SPD showed difficulties with sensory gating of N1 amplitudes only. Habituation analysis revealed significantly larger N2 amplitudes at tone 8 when compared to tone 2 among all groups suggesting that habituation does not occur for N2 amplitude among children in all three groups. A significant interaction occurred between tone and group for N1 amplitudes of children with SPD and the control group suggesting that the children in the control group did not habituate but the children in the SPD group did habituate. Analysis of N1 and N2 amplitude responses to tone 1 in a train without a deviant resulted in no significant differences among all three groups. However, while no differences were found between groups for the first tone, for N1 both HFA and TD groups had significant larger amplitude to the deviant tone in the 5th position, as compared to amplitude of brain response to the tone prior to the deviant. Children with SPD also had significantly larger N1 and N2 amplitudes to the deviant tones in the 4th and 5th positions, when compared to the amplitudes to the tone prior to the deviant. SPD and TD groups had an interaction at N2 amplitudes in the train with the deviant in the 4th positions. The SPD group displayed increased amplitudes at N2 to the deviant while TD decreased N2 amplitudes to the deviant. Regression analysis was conducted to assess relationships between the subtests of the TEA-Ch data and the neurological auditory processing phenomena. For the TD group this analysis revealed a strong relationship between attentional control/shift tasks and N2 amplitudes at tone 1 in the series without a deviant. For children with HFA, there was a significant relationship between attentional control/shift tasks and N1 amplitudes at tone 1 in the train without a deviant. Children with SPD also had a relationship between selective attention measures and N1 amplitudes at tone 1 in the train without a deviant. Results suggest that children with HFA, SPD and TD controls have distinct neuronal profiles related to attention. A better understanding of these group differences may help to elucidate the differential impact of auditory processing capacities on task performance in children with disabilities. This knowledge may inform how occupational therapists select therapeutic approaches, scaffold attention demands, and stimulate the adaptive response during interventions focused toward improving everyday task performance

Housing and the Macroeconomy

This dissertation studies the impact of several different housing market features on the macroeconomy. Chapter 1 augments the New-Keynesian model with collateral constraints to incorporate long-term debt in order to examine the interaction between multi-period loans, leverage, and indeterminacy. Allowing firms to borrow heavily against commercial housing by increasing the loan-to-value ratio from 0.01 to 0.90 reduces the level of steady state output approximately 3.19% and decreases social welfare. In contrast, increasing the debt limit of households increases steady state output by 2.72%. Social welfare is maximized under a utilitiarian function when households can borrow at a loan-to-value ratio of about 0.49. An economy with long-term debt also makes stabilization much more difficult for monetary policymakers because determinacy is harder to attain. Instead of only having to satisfy the Taylor Principle (which implies that a more than one-to-one response to inflation), central bankers must either use a strict inflation target or aggressively respond to inflation and the output gap to ensure determinacy. Chapter 2 examine a New-Keynesian model with housing where default occurs if housing prices are sufficiently low, resulting in a loss of access to credit and housing markets. Default decreases aggregate and patient household consumption, increases impatient household consumption, and amplifies the decline in housing prices due to a misallocation of housing. The effects on consumption often peak immediately before default occurs. Policies that prevent underwater borrowing or raise interest rates along with housing prices are generally desirable because they increase utilitarian social welfare. This paper shows that default is not simply a symptom of economic downturns, but a cause. Chapter 3 explores the correlation between the home mortgage interest deduction (HMID) and state economic growth. The HMID was introduced to incentivize home purchases by distorting the after-tax price, resulting in an overinvestment in real estate. Previous empirical work has shown that investment in physical capital increases economic growth more so than investment in structures. Theoretically, the anticipated effect of the HMID would be lower subsequent economic growth. However, this paper finds that residential housing is actually beneficial for economic growth