Bigraphical Arrangements

We define the bigraphical arrangement of a graph and show that the Pak-Stanley labels of its regions are the parking functions of a closely related graph, thus proving conjectures of Duval, Klivans, and Martin and of Hopkins and Perkinson. A consequence is a new proof of a bijection between labeled graphs and regions of the Shi arrangement first given by Stanley. We also give bounds on the number of regions of a bigraphical arrangement.Comment: Added Remark 19 addressing arbitrary G-parking functions; minor revision

Primer for the algebraic geometry of sandpiles

The Abelian Sandpile Model (ASM) is a game played on a graph realizing the dynamics implicit in the discrete Laplacian matrix of the graph. The purpose of this primer is to apply the theory of lattice ideals from algebraic geometry to the Laplacian matrix, drawing out connections with the ASM. An extended summary of the ASM and of the required algebraic geometry is provided. New results include a characterization of graphs whose Laplacian lattice ideals are complete intersection ideals; a new construction of arithmetically Gorenstein ideals; a generalization to directed multigraphs of a duality theorem between elements of the sandpile group of a graph and the graph's superstable configurations (parking functions); and a characterization of the top Betti number of the minimal free resolution of the Laplacian lattice ideal as the number of elements of the sandpile group of least degree. A characterization of all the Betti numbers is conjectured.Comment: 45 pages, 14 figures. v2: corrected typo

Physiological Responses in Initial Psychological Interviews

The purpose of this study was to determine the physiological responses of subjects to an initial psychological interview, and to study the effect of physical proximity and touch on these responses. Heart rate and total skin conductance variability were the responses monitored. To assess the subjects\u27 like or dislike of the psychologist interviewer, a measure of interpersonal attraction, the Interpersonal Judgment Scale, was employed. The California Psychological Inventory was utilized to investigate possible personality correlates with the physiological responses. Sixty females, between the ages of 18 and 28, responded to the California Psychological Inventory and were then connected to the physiological monitoring devices. The subjects\u27 physiological responses were recorded for a 10-minute period in an empty office and then they randomly received one of the following treatments: In treatment I the psychologist entered the counseling office, introduced himself, and sat one foot from the subject while orally administering the Rotter Incomplete Sentences Blank--Adult Form. When the psychologist reached item 15 he stated, Very good, now let\u27s go on to page 2. After the test, the psychologist said, That\u27s all for today, thank you for your help. If you will wait here, the experimenter will be right in. The psychologist then left the office, and the subject responded to the Interpersonal Judgment Scale. Treatment II was identical to treatment I, except the subject was touched three times during the interview, once on the shoulder and twice on the arm. In treatment III the psychologist entered the office, sat behind a desk and followed the procedure outlined in treatment I. The results indicated that a subject\u27s reaction to an initial psychological interview is a mild to moderate defensive response manifested by an increase in physiological stress levels. Total skin conductance variability increased significantly during the period when the psychologist was in the office. Heart rate increased in 54 out of 60 cases, but did not increase sufficiently enough in magnitude to justify significance. There were no significant differences between the three treatment groups on heart rate, skin conductance, or interpersonal attraction, and there were no personality correlates which were great enough to be of practical value. The data collected in the experiment supported the conclusion that a subject\u27s reaction to an initial psychological interview is a mild to moderate stress response manifested by increments in physiological stress levels. Touch and physical proximity do not appear to alter the stress response or the subject\u27s like--dislike attitude toward the psychologist

Sandpiles and Dominos

We consider the subgroup of the abelian sandpile group of the grid graph consisting of configurations of sand that are symmetric with respect to central vertical and horizontal axes. We show that the size of this group is (i) the number of domino tilings of a corresponding weighted rectangular checkerboard; (ii) a product of special values of Chebyshev polynomials; and (iii) a double-product whose factors are sums of squares of values of trigonometric functions. We provide a new derivation of the formula due to Kasteleyn and to Temperley and Fisher for counting the number of domino tilings of a 2m x 2n rectangular checkerboard and a new way of counting the number of domino tilings of a 2m x 2n checkerboard on a M\"obius strip.Comment: 35 pages, 24 figure

Emergency Responders\u27 Perceptions of Mental Health Patients While Providing Care in Rural Areas

Prior research has shown a correlation between public stigma and emergency responders\u27 perceptions of mental health patients while providing care. However, research examining public stigma and emergency responders\u27 perceptions of mental health patients is limited in rural areas. The purpose of this study was to explore possible relationships between the dependent variable, public stigma, and the independent variables: social distance, blameworthiness, and fear of unpredictable behavior. Link\u27s modified labeling theory was the theoretical framework for this study. A sample of 92 emergency responders obtained from Facebook completed a questionnaire that consisted of three Likert scales. A multiple regression showed little correlation between public stigma and social distance, blameworthiness, and fear of unpredictable behavior. Only .077 of the variance in public stigma was explained by the combination of independent variables. This study has demonstrated a possible shift in societal attitudes toward mental illness. It is important to determine the cause of this change in results so that continued education regarding mental health awareness may positively affect social change

How Teachers Modify their Instruction for Education for Employment Students Integrated into Regular Academic Programs at Smithfield High School

The research goals of this study were to determine: 1. What factors determine curriculum modifications by Smithfield High School teachers who instruct and evaluate the academic performance of the Education for Employment student