Morphic words and equidistributed sequences

The problem we consider is the following: Given an infinite word $w$ on an ordered alphabet, construct the sequence $\nu_w=(\nu[n])_n$, equidistributed on $[0,1]$ and such that $\nu[m]<\nu[n]$ if and only if $\sigma^m(w)<\sigma^n(w)$, where $\sigma$ is the shift operation, erasing the first symbol of $w$. The sequence $\nu_w$ exists and is unique for every word with well-defined positive uniform frequencies of every factor, or, in dynamical terms, for every element of a uniquely ergodic subshift. In this paper we describe the construction of $\nu_w$ for the case when the subshift of $w$ is generated by a morphism of a special kind; then we overcome some technical difficulties to extend the result to all binary morphisms. The sequence $\nu_w$ in this case is also constructed with a morphism. At last, we introduce a software tool which, given a binary morphism $\varphi$, computes the morphism on extended intervals and first elements of the equidistributed sequences associated with fixed points of $\varphi$

Bowling Together by Bowling Alone: Social Capital and COVID-19

Social capital describes the social bonds that exist within a community and comprises norms of reciprocity and trust as well as social relationships and social networks. We use data from counties in the United States to identify if community level responses to COVID-19 during the early phase of the pandemic (February 17 – May 10) depended on levels of social capital. We find that individuals who lived in counties with high levels of social capital reduced mobility faster than individuals living in counties with low levels of social capital and that they especially reduced mobility directed at retail and recreational activities, i.e. non-essential activities with higher potential risk. Difference-in-difference results show that the adoption of shelter-in-place orders (SIPOs) in a county, an increase in the number of diagnosed COVID-19 cases and a rainy weather were all associated with a decline in mobility, but that effects were heterogenous and depended on community level social capital. Effects were more pronounced in high social capital communities. Based on these findings, we map the level of vulnerability of communities in the United States to COVID-19: counties with a large share of the population suffering from pre-existing medical conditions and low levels of community level social capital are especially susceptible to experiencing severe health outcomes because of COVID-19

Assessment of the susceptibility of roads to flooding based on geographical information – test in a flash flood prone area (the Gard region, France)

International audienceIn flash flood prone areas, roads are often the first assets affected by inundations which make rescue operations difficult and represent a major threat to lives: almost half of the victims are car passengers trapped by floods. In the past years, the Gard region (France) road management services have realized an extensive inventory of the known road sub- mersions that occurred during the last 40 years. This inven- tory provided an unique opportunity to analyse the causes of road flooding in an area frequently affected by severe flash floods. It will be used to develop a road submersion suscep- tibility rating method, representing the first element of a road warning system.This paper presents the results of the analysis of this data set. A companion paper will show how the proposed road susceptibility rating method can be combined with dis- tributed rainfall-runoff simulations to provide accurate road submersion risk maps.The very low correlation between the various possible ex- planatory factors and the susceptibility to flooding measured by the number of past observed submersions implied the use of particular statistical analysis methods based on the general principals of the discriminant analysis.The analysis led to the definition of four susceptibility classes for river crossing road sections. Validation tests con- firmed that this classification is robust, at least in the con- sidered area. One major outcome of the analysis is that the susceptibility to flooding is rather linked to the location of the road sections than to the size of the river crossing structure (bridge or culvert)

Finite-size scaling in thin Fe/Ir(100) layers

The critical temperature of thin Fe layers on Ir(100) is measured through M\"o{\ss}bauer spectroscopy as a function of the layer thickness. From a phenomenological finite-size scaling analysis, we find an effective shift exponent lambda = 3.15 +/- 0.15, which is twice as large as the value expected from the conventional finite-size scaling prediction lambda=1/nu, where nu is the correlation length critical exponent. Taking corrections to finite-size scaling into account, we derive the effective shift exponent lambda=(1+2\Delta_1)/nu, where Delta_1 describes the leading corrections to scaling. For the 3D Heisenberg universality class, this leads to lambda = 3.0 +/- 0.1, in agreement with the experimental data. Earlier data by Ambrose and Chien on the effective shift exponent in CoO films are also explained.Comment: Latex, 4 pages, with 2 figures, to appear in Phys. Rev. Lett

After the War is Over Will There Be Any Home Sweet Home?

https://digitalcommons.library.umaine.edu/mmb-vp/1153/thumbnail.jp

Size effect on magnetism of Fe thin films in Fe/Ir superlattices

In ferromagnetic thin films, the Curie temperature variation with the thickness is always considered as continuous when the thickness is varied from $n$ to $n+1$ atomic planes. We show that it is not the case for Fe in Fe/Ir superlattices. For an integer number of atomic planes, a unique magnetic transition is observed by susceptibility measurements, whereas two magnetic transitions are observed for fractional numbers of planes. This behavior is attributed to successive transitions of areas with $n$ and $n+1$ atomic planes, for which the $T_c$'s are not the same. Indeed, the magnetic correlation length is presumably shorter than the average size of the terraces. Monte carlo simulations are performed to support this explanation.Comment: LaTeX file with Revtex, 5 pages, 5 eps figures, to appear in Phys. Rev. Let

A Comparative Analysis of the Academic Performance of Native and Transfer Students

Results of a study comparing the academic performance of native and transfer students

The Math Placement Tests: Relationships to Mathematics Course Performance, Mathematics Course Selection, and Other Predictors of Academic Achievement

The effectiveness of the Math Placement Tests (Intermediate and Advanced) is anayzed

The Math Placement Tests: Relationships to Mathematics Course Performance, Mathematics course Selection, and Other Predictors of Academic Achievement

Executive Summary: The Math Placement Tests have been used by all four-year institutions in the state of Washington to aid in the placement of students into their first college-level mathematics course since 1984. This report was prepared in response to concerns of Western Washington University\u27s Mathematics Department regarding the usefulness of. the placement tests in correctly placing students in mathematics courses. The relationships of the math placement tests to final mathematics course grade and other indicators of academic achievement, including high school GPA, WPCT-Q score, and SAT-M score were evaluated. The math placement tests were found to be moderately positively related to final grade and each of the three indicator variables. The math placement tests were not, in most cases, superior to high school GPA andjor WPCT-Q score in prediction of final mathematics course grade. The percentage of students who passed (earned a grade of c¬ or better) their mathematics course varied depending on the course in which they enrolled, which placement test they took, and the score they received on the placement test. The probability of receiving a c- or better among those who took the Intermediate Algebra Test ranged from a low of 48.2 percent in Math 103 to a high of 72.4 percent in Math 155. The chance of passing a mathematics course for those who took the Pre-Calculus Test ranged from a low of 63.5 percent in Math 103 to a high of 90.9 in Math 104. In general, the probability of receiving a passing grade increased with higher Math Placement Test scores. For a number of courses, the current cut-off score on the Intermediate Algebra Test may be too low. students who enrolled with scores below, at, or slightly above these cut-offs had, in many cases, only a slim chance of passing the course. Conversely, cut-off scores on the Pre-Calculus Test for admission to many courses were too high. Students who had a reasonable chance of passing these courses would be denied admission based on the current cut-off points. It is suggested that the current cut-off scores be re-evaluated and when new cut-offs are decided upon, that they be more strictly adhered to

A Comparative Analysis of the Academic Performance of Native and Transfer Students

Executive Summary: This study utilized the records of two samples of wwu upper¬ division students (those with 90 credits and above) to evaluate the relationships of academic performance to students\u27 admission status (either native or transfer) and other selected student characteristics such as gender, ethnicity, and age. The first sample measured academic performance in terms of cumulative WWU GPA. The second sample looked at grades earned in 300 and 400 level courses only (upper-division GPA). This report was prepared as a follow-up to an earlier study that used a much more limited sample. Females were found to have consistently higher GPAs than males, regardless of the sample or the type of GPA (cumulative or upper-division) used in the analysis. Older students generally outperformed younger students although the relationship between age and academic performance was mediated by a student\u27s admission status. Students of a given age but with different admission statuses or of the same admission status but of different ages in many cases did not have equivalent GPAs. In general, among younger students natives outperformed two-year transfer students. No such difference was found among older students. This study also found differences in both the cumulative GPA and the upper-division GPA earned by different ethnic groups. Caucasians had a higher average cumulative GPA than Blacks and a higher average upper-division GPA than both Blacks and Asians. In addition, American Indian students also had a higher average upper-division GPA than Black students. A student\u27s grade point average when he or she enters Western (high school GPA for natives and GPA at the institution attended before transferring to Western for transfer students) was the best predictor of how well a student would do academically once at Western. WPCT subtest scores also aided in the prediction of both cumulative and upper-division GPAs for both native and transfer students. However, the relative importance of these subtests was different for students of different admission statuses. Prediction of native students\u27 academic performance was most enhanced by the WPCT-Verbal subtest score whereas prediction of a transfer student\u27s academic performance was more improved by the knowledge of his or her WPCT-Quantitative subtest score. After conducting several separate analyses of the differences and similarities of WWU\u27s native and transfer students, it can be concluded that when comparing students of different admission statuses regardless of age there is effectively no difference in the academic performance of Western\u27s native and two-year transfer students