All Items 103

Teaching the next generation of statistics students to "think with data": Special issue on statistics and the undergraduate curriculum

Horton, Nicholas J. (Department of Mathematics and Statistics, Amherst College)

Teaching the next generation of statistics students to "think with data": Special issue on statistics and the undergraduate curriculum
Ensuring that mathematics is relevant in a world of data science

Horton, Nicholas J. (Department of Mathematics and Statistics, Amherst College)

The recent growth of data science has been remarkable. Analysts now have rich data and powerful computational tools to help answer important questions. Examples of ways that insights can be wrangled from this information abound in diverse areas. This has led some to dub computational thinking (or fluency) as the "new literacy" on par with writing and quantitative skills. A major unanswered question relates to the role of mathematics in the training of future data scientists. How can we be sure that data science is on a firm mathematical and statistical foundation? In the article, we will consider what courses in mathematics would best prepare future data scientists.

Ensuring that mathematics is relevant in a world of data science
Exploring the sterically disfavored binding of acetylene to a geminal olefinic hydrogen-fluorine atom pair: The microwave spectrum and molecular structure of cis-1,2-difluoroethylene–acetylene

Leung, Helen O. (Department of Chemistry, Amherst College)

The microwave rotational spectrum of the gas-phase bimolecular heterodimer formed between cis-1,2-difluoroethylene and acetylene is obtained using Fourier transform microwave spectroscopy from 5.9 to 21.2 GHz. Rotational constants derived from the analysis of the spectra for the normal isotopologue and singly substituted ¹³C isotopologues, obtained in natural abundance, allow the determination of the structure of the complex, which, in the absence of a fluorine-hydrogen atom pair located cis to each other, adopts a sterically disfavored geometry (“side-binding”) in which the acetylene interacts with a geminal fluorine-hydrogen atom pair. Structural details are found to be similar to those of previously studied heterodimers with side-binding of acetylene to fluorine while reflecting the degree of halosubstitution. A detailed comparison with the (Z)-1-chloro-2-fluoroethylene-acetylene complex reveals information regarding the relaxed steric requirements for hydrogen bonding to chlorine as opposed to hydrogen bonding to fluorine.

Exploring the sterically disfavored binding of acetylene to a geminal olefinic hydrogen-fluorine atom pair: The microwave spectrum and molecular structure of cis-1,2-difluoroethylene–acetylene
Justin Perkins letter to Asa Bullard, 1837 July 20

Perkins, Justin, 1805-1869

J. Perkins letter or draft of a letter to Asa Bullard in which Perkins responds to a letter from Bullard and remarks on his recovered health. He assures Bullard that decisions regarding publication of letters he sends Bullard are entirely up to Bullard's judgement. He concludes by saying that on this sheet he sends Bullard a short account of their Sabbath School. Following the letter is the account in which describes the Sabbath School of the Nestorian Mission and mentions Dr. Grant and Mar Yohanna (also called Mar Yohannan). The account was published with some variations in the February 1838 issue of the Sabbath School Visiter.

Justin Perkins letter to Asa Bullard, 1837 July 20
A Modal Argument Against Vague Objects

Moore, Joseph Gwyer (Department of Philosophy, Amherst College)

There has been much discussion of whether there could be objects A and B that are “individuatively vague” in the following way: object A and object B neither determinately stand in the relation of identity to one another, nor do they determinately fail to stand in this relation. If there are objects of this type, then we would have a genuine case of metaphysical vagueness, or “vagueness-in-the-world.” The possibility of vague objects in this sense strikes many as incoherent. The possibility’s very description not only seems to talk of two objects but, much worse, it seems to point to a feature that distinguishes them: unlike object A, object B is not determinately identical to object A. This suspicion of incoherence is voiced in the famous arguments given against the possibility by Gareth Evans and Nathan Salmon. But the status of those arguments and others is uncertain. Here I present a new argument against vague objects — or more precisely, against the possibility of individuatively vague objects that satisfy an important and common additional condition that I will call “Democracy.” Since my argument turns on a connection between what is indeterminate and what is possible, I call it “the modal argument.”.

A Modal Argument Against Vague Objects
Saving substitutivity in simple sentences

Moore, Joseph Gwyer (Department of Philosophy, Amherst College)

Saving substitutivity in simple sentences
What do college students want?: A student-centered approach to multifaith involvement

Sorrentino, Paul V. (Office of Religious & Spiritual Life, Amherst College)

The author presents research findings about the preferences of college students as they consider coming together with people of other faiths in multifaith settings. He discusses what works well and what does not. Select quotations from interviews are included. The author suggests a practical model for multifaith work on campus based on the principles represented in the acronym “RAM.” Multifaith involvement should include being Respectful toward the beliefs of others, being Authentic to one’s own tradition, and having Meaningful interreligious interaction.

What do college students want?: A student-centered approach to multifaith involvement
Voluntary exercise can strengthen the circadian system in aged mice

Leise, Tanya L. (Department of Mathematics and Statistics, Amherst College)

Consistent daily rhythms are important to healthy aging according to studies linking disrupted circadian rhythms with negative health impacts. We studied the effects of age and exercise on baseline circadian rhythms and on the circadian system's ability to respond to the perturbation induced by an 8 h advance of the light:dark (LD) cycle as a test of the system's robustness. Mice (male, mPer2luc/C57BL/6) were studied at one of two ages: 3.5 months (n=39) and >18 months (n=72). We examined activity records of these mice under entrained and shifted conditions as well as mPER2::LUC measures ex vivo to assess circadian function in the suprachiasmatic nuclei (SCN) and important target organs. Age was associated with reduced running wheel use, fragmentation of activity, and slowed resetting in both behavioral and molecular measures. Furthermore, we observed that for aged mice, the presence of a running wheel altered the amplitude of the spontaneous firing rate rhythm in the SCN in vitro. Following a shift of the LD cycle, both young and aged mice showed a change in rhythmicity properties of the mPER2::LUC oscillation of the SCN in vitro, and aged mice exhibited longer lasting internal desynchrony. Access to a running wheel alleviated some age-related changes in the circadian system. In an additional experiment, we replicated the effect of the running wheel, comparing behavioral and in vitro results from aged mice housed with or without a running wheel (>21 months, n=8 per group, all examined 4 days after the shift). The impact of voluntary exercise on circadian rhythm properties in an aged animal is a novel finding and has implications for the health of older people living with environmentally induced circadian disruption.

Voluntary exercise can strengthen the circadian system in aged mice
Two-photon vibrational transitions in ¹⁶O₂⁺ as probes of variation of the proton-to-electron mass ratio

Carollo, Ryan A. (Department of Physics and Astronomy, Amherst College)

Vibrational overtones in deeply-bound molecules are sensitive probes for variation of the proton-to-electron mass ratio μ. In nonpolar molecules, these overtones may be driven as two-photon transitions. Here, we present procedures for experiments with ¹⁶O⨧ including state-preparation through photoionization, a two-photon probe, and detection. We calculate transition dipole moments between all X²∏g vibrational levels and those of the A²∏ᵤ excited electronic state. Using these dipole moments, we calculate two-photon transition rates and AC-Stark-shift systematics for the overtones. We estimate other systematic effects and statistical precision. Two-photon vibrational transitions in ¹⁶O⨧ provide multiple routes to improved searches for μ variation.

Two-photon vibrational transitions in ¹⁶O₂⁺ as probes of variation of the proton-to-electron mass ratio
The death of historical memory? Javier Cercas's El impostor versus the legacy of Spaniards deported to Nazi camps

Brenneis, Sara J. (Spanish Department, Amherst College)

Javier Cercas criticizes what he calls “the so-called memory industry” in his 2014 book, El impostor. While delving into the life story of Enric Marco, who was unmasked in 2005 as a false survivor of the Nazi concentration camp Flossenbürg, Cercas pronounces historical memory dead in Spain. This article retraces Marco’s rise to fame against the backdrop of Spain’s relevance to the Holocaust as well as seven decades of narratives by actual Spanish survivors of Nazi concentration camps published inside the country. These narratives have given increased visibility to Spanish deportees, forming a core aspect of Spain’s historical memory. Countering Cercas’s claim of morbidity, this article demonstrates that the recuperation of historical memory has moved from a grassroots movement to a legislative initiative and back again in Spain, particularly as concerns the legacy of Spanish Republicans deported to Nazi camps. Cercas’s misplaced glorification of a false survivor and his narrow focus on the recuperation of historical memory as a collective memory of the Spanish Civil War and Franco dictatorship governed by the Law of Historical Memory notwithstanding, the movement has had a trickle-down effect on the visibility of the history of Spaniards deported to Nazi camps during World War II.

The death of historical memory? Javier Cercas's El impostor versus the legacy of Spaniards deported to Nazi camps
On Gauss's First Proof of the Fundamental Theorem of Algebra

Velleman, Daniel J. (Department of Mathematics and Statistics, Amherst College, Department of Mathematics and Statistics, University of Vermont)

Carl Friedrich Gauss is often given credit for providing the first correct proof of the fundamental theorem of algebra in his 1799 doctoral dissertation. However, Gauss’s proof contained a significant gap. In this paper, we give an elementary way of filling the gap in Gauss’s proof.

On Gauss's First Proof of the Fundamental Theorem of Algebra
The microwave spectrum and molecular structure of vinyl chloride-HCCH, a side-binding complex [Supporting information]

Marshall, Mark D. (Department of Chemistry, Amherst College)

Supporting information for "The microwave spectrum and molecular structure of vinyl chloride-acetylene, a side-binding complex."

The microwave spectrum and molecular structure of vinyl chloride-HCCH, a side-binding complex [Supporting information]
Ferrocenyl-amidinium compound as building block for aqueous proton-coupled electron transfer studies

Young, Elizabeth R. (Department of Chemistry, Amherst College)

A water-soluble amidinium-appended ferrocene moiety is characterized in which the amidinium functionality is fused directly to the ferrocene ring (Fcam1). This species is designed to form a building block for aqueous proton-coupled electron transfer in which proton transfer occurs to the bulk and electron transfer occurs to a chemical oxidant. pH-dependent absorption spectroscopy and electrochemistry show that the electrochemical potential is directly linked to the protonation state of the amidinium. A thermodynamic square scheme is constructed for Fcam1. The square scheme serves as motivation and provides direction for incorporating this species into a covalently-bound system for the study of proton-coupled electron transfer.

Ferrocenyl-amidinium compound as building block for aqueous proton-coupled electron transfer studies
The fundamental theorem of algebra: A visual approach

Velleman, Daniel J. (Department of Mathematics and Statistics, Amherst College)

The fundamental theorem of algebra says that for every nonconstant polynomial p with complex coefficients, there is a complex number z such that p(z) = 0. In this paper we present a method of visualizing functions on the complex plane, and use this method to illustrate why the fundamental theorem of algebra is true. We also discuss the history of the fundamental theorem of algebra and its proofs.

The fundamental theorem of algebra: A visual approach
High sensitivity to variation in the proton-to-electron mass ratio in O2+

Hanneke, David Andrew (Department of Physics and Astronomy, Amherst College)

Molecular vibrational transitions are prime candidates for model-independent searches for variation of the proton-to-electron mass ratio. Searches for present-day variation achieve the highest sensitivity with deep molecular potentials. We identify several high-sensitivity transitions in the deeply bound O2+ molecular ion. These transitions are electric-dipole forbidden and have narrow linewidths. The most sensitive transitions take advantage of an accidental degeneracy between vibrational states in different electronic potentials. We suggest experimentally feasible routes to a measurement with uncertainty below current limits on present-day variation in mp/me.

High sensitivity to variation in the proton-to-electron mass ratio in O2+
The gas-phase structure of the asymmetric, trans-dinitrogen tetroxide (N2O4), formed by dimerization of nitrogen dioxide (NO2), from rotational spectroscopy and ab initio quantum chemistry

Marshall, Mark D. (Department of Chemistry, Amherst College)

We report the first experimental gas-phase observation of an asymmetric, trans N2O4 formed by the dimerization of NO2. In additional to the dominant 14N2 16O4 species, rotational transitions have been observed for all species with single 15N and 18O substitutions, as well as several multiply substituted isotopologues. These transitions were used to determine a complete substitution structure as well as an r0 structure from the fitted zero-point averaged rotational constants. The determined structure is found to be that of an ON—O-NO2 linkage with the shared oxygen atom closer to the NO2 than the NO (1.42 vs 1.61 Å). The structure is found to be nearly planar with a trans O-N-O-N linkage. From the spectra of the 14N15NO4 species, we were able to determine the nuclear quadrupole coupling constants for each specific nitrogen atom. The equilibrium structure determined by ab initio quantum chemistry calculations is in excellent agreement with the experimentally determined structure. No spectral evidence of the predicted asymmetric, cis N2O4 was found in the spectra.

The gas-phase structure of the asymmetric, trans-dinitrogen tetroxide (N2O4), formed by dimerization of nitrogen dioxide (NO2), from rotational spectroscopy and ab initio quantum chemistry
Third-harmonic-generation of a diode laser for quantum control of beryllium ions

Carollo, Ryan A. (Department of Physics and Astronomy, Amherst College)

We generate coherent ultraviolet radiation at 313 nm as the third harmonic of an external-cavity diode laser. We use this radiation for laser cooling of trapped beryllium atomic ions and sympathetic cooling of co-trapped beryllium-hydride molecular ions. An LBO crystal in an enhancement cavity generates the second harmonic, and a BBO crystal in a doubly resonant enhancement cavity mixes this second harmonic with the fundamental to produce the third harmonic. Each enhancement cavity is preceded by a tapered amplifier to increase the fundamental light. The 36-mW output power of this all-semiconductor-gain system will enable quantum control of the beryllium ions' motion.

Third-harmonic-generation of a diode laser for quantum control of beryllium ions
Distortion product otoacoustic emissions and intracranial pressure during CSF infusion testing

Horton, Nicholas J. (Department of Mathematics and Statistics, Amherst College)

Background: A noninvasive method to monitor changes in intracranial pressure (ICP) is required for astronauts on long-duration spaceflight who are at risk of developing the Visual Impairment/Intracranial Pressure syndrome that has some, but not all of the features of idiopathic intracranial hypertension. We assessed the validity of distortion product otoacoustic emissions (DPOAEs) to detect changes in ICP. Methods: Subjects were eight patients undergoing medically necessary diagnostic cerebrospinal fluid (CSF) infusion testing for hydrocephalus. DPOAE measurements were obtained with an FDA-approved system at baseline and six controlled ICP levels in ∼3 mmHg increments in random order, with a range from 10.8 ± 2.9 mmHg (SD) at baseline to 32.3 ± 4.1 mmHg (SD) at level 6. Results: For f2 frequencies between 800 and 1700 Hz, when ICP was ≥ 12 mmHg above baseline ICP, DPOAE angles increased significantly and DPOAE magnitudes decreased significantly, but less robustly. Discussion: Significant changes in DPOAE angle and magnitude are seen when ICP is ≥ 12 mmHg above a subject's supine baseline ICP during CSF infusion testing. These results suggest that the changes in DPOAE angle and magnitude seen with change in ICP are physiologically based, and suggest that it should be possible to detect pathological ICP elevation using DPOAE measurements. To use DPOAE for noninvasive estimation of ICP during spaceflight will require baseline measurements in the head-up, supine, and head-down positions to obtain baseline DPOAE values at different ICP ranges

Distortion product otoacoustic emissions and intracranial pressure during CSF infusion testing
Making progress in a crowded market

Horton, Nicholas J. (Department of Mathematics and Statistics, Amherst College)

In their wide-ranging, insightful and provocative paper, Ograjenšek Gal (2016) restate and enunciate our shared goal to help motivate students to learn to use data to provide answers to real-world problems. They also provide specific suggestions about additional ways to create more opportunities for scaffolding and practice of qualitative thinking in our courses and curriculum. I commend them for this guidance—which is wholly consistent with the sentiments of many—including Brown Kass (2009), the INGEnIOuS project, http://www.ingeniousmathstat.org and Cobb (2015). All suggest a broad definition of statistics, encourage efforts to ensure that statistics is a vibrant choice for students and call for major (radical?) changes to our curriculum to support this shift. While there have been major efforts in recent years to adapt our curriculum to provide exposure to the excitement of statistics [see for example several of the rich datasets in Gould, (2010)], students need to be more directly engaged with a broad range of new data-related topics to be successful in our increasingly diverse discipline (Horton, 2016; Ridgway, 2015). The growth of data science poses many challenges and opportunities. As the authors describe, to be relevant in this world awash in data, statistics students need exposure to quantitative and qualitative approaches for the planning and design of studies, conduct and analysis, as well as interpretation and communication of results and implications. I will briefly consider the implications of this paper as well as barriers for implementation of the approaches enunciated in this paper in two distinct areas: (1) our introductory courses as well as (2) our undergraduate programs in statistics.

Making progress in a crowded market
Reflectance measures from infant ears with normal hearing and transient conductive hearing loss

Horton, Nicholas J. (Department of Mathematics and Statistics, Amherst College)

Objective: The objective is to develop methods to utilize newborn reflectance measures for the identification of middle-ear transient conditions (e.g., middle-ear fluid) during the newborn period and ultimately during the first few months of life. Transient middle-ear conditions are a suspected source of failure to pass a newborn hearing screening. The ability to identify a conductive loss during the screening procedure could enable the referred ear to be either (1) cleared of a middle-ear condition and recommended for more extensive hearing assessment as soon as possible, or (2) suspected of a transient middle-ear condition, and if desired, be rescreened before more extensive hearing assessment. Design: Reflectance measurements are reported from full-term, healthy, newborn babies in which one ear referred and one ear passed an initial auditory brainstem response newborn hearing screening and a subsequent distortion product otoacoustic emission screening on the same day. These same subjects returned for a detailed follow-up evaluation at age 1 month (range 14 to 35 days). In total, measurements were made on 30 subjects who had a unilateral refer near birth (during their first 2 days of life) and bilateral normal hearing at follow-up (about 1 month old). Three specific comparisons were made: (1) Association of ear's state with power reflectance near birth (referred versus passed ear), (2) Changes in power reflectance of normal ears between newborn and 1 month old (maturation effects), and (3) Association of ear's newborn state (referred versus passed) with ear's power reflectance at 1 month. In addition to these measurements, a set of preliminary data selection criteria were developed to ensure that analyzed data were not corrupted by acoustic leaks and other measurement problems. Results: Within 2 days of birth, the power reflectance measured in newborn ears with transient middle-ear conditions (referred newborn hearing screening and passed hearing assessment at age 1 month) was significantly greater than power reflectance on newborn ears that passed the newborn hearing screening across all frequencies (500 to 6000 Hz). Changes in power reflectance in normal ears from newborn to 1 month appear in approximately the 2000 to 5000 Hz range but are not present at other frequencies. The power reflectance at age 1 month does not depend significantly on the ear's state near birth (refer or pass hearing screening) for frequencies above 700 Hz; there might be small differences at lower frequencies. Conclusions: Power reflectance measurements are significantly different for ears that pass newborn hearing screening and ears that refer with middle-ear transient conditions. At age 1 month, about 90% of ears that referred at birth passed an auditory brainstem response hearing evaluation; within these ears the power reflectance at 1 month did not differ between the ear that initially referred at birth and the ear that passed the hearing screening at birth for frequencies above 700 Hz. This study also proposes a preliminary set of criteria for determining when reflectance measures on young babies are corrupted by acoustic leaks, probes against the ear canal, or other measurement problems. Specifically proposed are "data selection criteria" that depend on the power reflectance, impedance magnitude, and impedance angle. Additional data collected in the future are needed to improve and test these proposed criteria.

Reflectance measures from infant ears with normal hearing and transient conductive hearing loss