Mathematics is viewed as essential to the economic competitiveness of the United States on the global stage (US Department of Education). As a part of the core Science, Technology, Engineering and Mathematics (STEM) fields, mathematics is vital to the nation's economic prosperity, yet enrollment in STEM fields at the college/university level has remained relatively stable, despite millions of dollars expended to improve STEM education and retention. Most extant research focuses on innovations within classroom settings that can improve learning outcomes for students pursuing STEM majors. Additional research is needed in examining how the sequencing of courses taken by students can help or hinder their progress toward the successful completion of a STEM degree. In this first phase of our research, quantitative analytics was used to identify the impact of specific courses on students' risk of dropping out of a Math major. Findings suggest a general inverse correlation between academic performance and attrition: good performance predicts lower attrition rates. Survival analysis indicated that the further a student goes within the math major, the greater the risk of dropping out. Students in a Math major tend to be more likely to drop out after their 4th year compared to their first three years. In general, students show increased inclination to switch majors from their second year and those students who have stayed in the program for too long are very likely to switch to another major.

Neutron-based methods of bulk material analysis are used to detect contraband in cargo, characterize coal and cement, and identify unexploded ordnance, among other applications. Characteristic gamma rays produced in nuclear reactions (inelastic neutron scattering, thermal neutron capture, and activation) initiated by 14-MeV neutrons in the volume of an irradiated object are utilized for its elemental identification. In many situations, automated methods of spectral analysis and decision analytics are required. In this study, a spectrum analysis technique based on wavelets was developed, which determines elemental intensities using peak areas corresponding to characteristic photons. The algorithm was evaluated using experimental data measured with a 14-MeV pulse neutron source and high-resolution and low-resolution photon detectors. It was shown that this technique provides quick, accurate, and objective analysis of gamma-ray spectra.

The unicellular green alga Chlamydomonas reinhardtii has long served as model organism for studies on the circadian clock. This clock is present in all eukaryotes and some prokaryotes allowing them to anticipate and take advantage of the daily oscillations in the environment. Although much is known about the circadian clock in C reinhardtii, the photoreceptors mediating entrainment of the clock to the daily changes of light remain obscure. Based on its circadian rhythm of phototaxis as a reporter of the clock's phase, we show here that C reinhardtii strain CC-124 is highly sensitive to blue light of 440 nm when resetting its circadian clock upon light pulses. Thus, CC-124 differs in this respect from what was previously reported for a cell wall-deficient strain. An action spectrum analysis revealed that CC-124 also responds with high sensitivity to green (540 nm), red (640-660 nm), and possibly UV-A (<= 400 nm) light, and therefore shows similarities as well to what has been reported for the cell wall-deficient strain. We also investigated two RNA interference strains with reductions in the level of the blue light photoreceptor plant cryptochrome (CPH1). One of them, the strain with the greater reduction, surprisingly showed an increased sensitivity in clock resetting upon blue light pulses of 440 nm. This increase in sensitivity reverted to wild-type levels when the RNA interference strain reverted to wild-type protein levels. It suggests that plant cryptochrome in C reinhardtii could function as negative rather than positive modulator of circadian clock resetting. (C) 2013 Elsevier Masson SAS. All rights reserved.

Automated monitoring of circadian rhythms is an efficient way of gaining insight into oscillation parameters like period and phase for the underlying pacemaker of the circadian clock. Measurement of the circadian rhythm of phototaxis (swimming towards light) exhibited by the green alga Chlamydomonas reinhardtii has been automated by directing a narrow and dim light beam through a culture at regular intervals and determining the decrease in light transmittance due to the accumulation of cells in the beam. In this study, the monitoring process was optimized by constructing a new computer-controlled measuring machine that limits the test beam to wavelengths reported to be specific for phototaxis and by choosing an algal strain, which does not need background illumination between test light cycles for proper expression of the rhythm. As a result, period and phase of the rhythm are now unaffected by the time a culture is placed into the machine. Analysis of the rhythm data was also optimized through a new algorithm, whose robustness was demonstrated using virtual rhythms with various noises. The algorithm differs in particular from other reported algorithms by maximizing the fit of the data to a sinusoidal curve that dampens exponentially. The algorithm was also used to confirm the reproducibility of rhythm monitoring by the machine. Machine and algorithm can now be used for a multitude of circadian clock studies that require unambiguous period and phase determinations such as light pulse experiments to identify the photoreceptor(s) that reset the circadian clock in C. reinhardtii.

During the 2008‐2009 academic year, the author embarked on an extremely non-standard curriculum path: developing comic books with embedded mathematics appropriate for 3rd through 6th grade students. With the help of an education professor to measure impact, an elementary-school principal, and talented undergraduate illustrators, this project came to fruition and the comics were implemented in elementary classrooms at Cumberland Trace Elementary in the Warren County School System in Bowling Green, Kentucky. This manuscript gives the history of this idea, the difficulties of developing the content of the comics and getting them illustrated, and the implementation plan in the school.

Since the advent of techniques to investigate gene expression on a large scale, numerous circadian rhythms in mRNA amount have been reported. These rhythms generally differ in amplitude and phase. The authors investigated how far a parameter not regulated by the circadian clock can influence the phase of a rhythm in RNA amount arising from a circadian rhythm of transcription. Using a discrete-time approach, they modeled a sinusoidal rhythm in transcription with various constant exponential RNA decay rates. They found that the slower the RNA degradation, the later the phase of the RNA amount rhythm compared with the phase of the transcriptional rhythm. However, they also found that the phase of the RNA amount rhythm is limited to a timeframe spanning the first quarter of the period following the phase of the transcriptional rhythm. This finding is independent of the amplitude and vertical shift of the transcriptional rhythm or even of the way constant RNA degradation is modeled. The authors confirmed their results with a continuous-time model, which allowed them to derive a simple formula relating the phase of the RNA amount rhythm solely to the phase and period of its sinusoidal transcriptional rhythm and its constant RNA half-life. This simple formula even holds true for the best sinusoidal approximations of a nonsinusoidal rhythm of transcription and RNA amount. When expanding the model to include additional events with constant exponential kinetics, such as RNA processing, they found that each event expands the phase limit by another quarter of the period when it occurs in sequence but not when it occurs as a competing process. However, the limit expansion comes at the price of minuscule amplitudes. When using a discrete-time approach to model constant rates of transcription with a sinusoidal RNA half-life, the authors found that the phase of the RNA amount rhythm is unaffected by changes in the constant rate of transcription. In summary, their data show that at least 4 distinct circadian regulatory mechanisms are required to allow for all phases in rhythms of RNA amount, one for each quarter of the period.

If a large number of educated people were asked, “What was your most exciting class?”, odds are that very few of them would answer “Trigonometry.” The subject is generally presented in a less-than-exciting fashion, with the repeated caveat that “you’ll need this when you take calculus,” or “this has lots of applications” without ever really seeing many of them. This manuscript addresses how the author is trying to change this tradition by exposing casual students from kindergarten to college to Joseph Fourier’s secret, that nearly any function can be built out of sine and cosine curves. And music serves as a both the bait that entices the student to learn, and the hook.

Geronimo, Hardin et al. have previously constructed orthogonal and biorthogonal scaling vectors by extending a spline scaling vector with functions supported on [0,1]. Many of these constructions occurred before the concept of balanced scaling vectors was introduced. This paper will show that adding functions on [0,1] is insufficient for extending spline scaling vectors to scaling vectors that are both orthogonal and balanced. We are able, however, to use this technique to extend spline scaling vectors to balanced, biorthogonal scaling vectors, and we provide two large classes of this type of scaling vector, with approximation order two and three, respectively, with two specific constructions with desirable properties in each case. The constructions will use macroelements supported on [0,1], some of which will be fractal functions.

The main result of this paper is the creation of an orthogonal scaling vector of four differentiable functions, two supported on [−1, 1] and two supported on [0, 1], that generates a space containing the classical spline space S1 3 (Z) of piecewise cubic polynomials on integer knots with one derivative at each knot. The author uses a macroelement approach to the construction, using differentiable fractal function elements defined on [0, 1] to construct the scaling vector. An application of this new basis in an image compression example is provided. AMS Subject Classification Numbers: 42C40, 65D15

We develop a macroelement based technique for constructing orthogonal univariate multiwavelets. We illustrate the technique with two examples. In the first example we provide a new construction of the symmetric, orthogonal, continuous scaling vector given in [1]. In the second example we review the construction of a continuous orthogonal scaling vector with three components. The components of this scaling vector are symmetric or antisymmetric and provide approximation order 3 from [2].

In Kessler (Appl. Comput. Harmonic Anal.9 (2000), 146–165), a construction was given for a class of orthogonal compactly supported scaling vectors on R2, called short scaling vectors, and their associated multiwavelets. The span of the translates of the scaling functions along a triangular lattice includes continuous piecewise linear functions on the lattice, although the scaling functions are fractal interpolation functions and possibly nondifferentiable. In this paper, a similar construction will be used to create biorthogonal scaling vectors and their associated multiwavelets. The additional freedom will allow for one of the dual spaces to consist entirely of the continuous piecewise linear functions on a uniform subdivision of the original triangular lattice.