A Study of Prospective Secondary Mathematics Teachers’ Evolving Understanding of Reasoning-and-Proving

Proof is a foundational mathematical activity that has been underrepresented in school mathematics. The recently adopted Common Core State Standards in Mathematics includes eight process standards, several of which promote the inclusion of reasoning and proof across all grades, courses, and students. If students are to reach the expectations recommended by mathematics researchers and explicitly identified in the Common Core State Standards, then students will need opportunities to construct and validate proof arguments. However, secondary students find it challenging to validate arguments and produce proofs and do not know what a mathematical proof is. Furthermore, those preparing to be secondary mathematics teachers in undergraduate mathematics courses are unable to construct proofs on a consistent basis, and practicing secondary teachers possess a limited conception of proof. A six-week graduate-level course was taught with the purpose of increasing practicing mathematics teachers’ knowledge, expanding their conceptions of reasoning and proof, and preparing them to create similar experiences for their students. Research was conducted on the course to study the participants’ evolving understanding of reasoning-and-proving. The results suggest that: 1) the course was successful at expanding the participants conception of proof; 2) the prospective teachers encountered five challenges when asked to write proofs that are at the secondary mathematics level; 3) specific types of arguments were challenging for participants to classify as proofs or non-proofs; and 4) even though the participants were skillful in selecting high-level tasks that they could modify to include reasoning-and-proving opportunities, more work is needed to integrate such task across any secondary curricula

On the Security of Doubly Efficient PIR

Doubly Efficient Private Information Retrieval (DEPIR) enables queries to an externally held database while hiding the identity of the queried indices, strengthening standard Private Information Retrieval (Chor, Goldreich, Kushilevitz, Sudan FOCS\u2795) with an efficiency requirement that the computational demands of both client and server are sublinear in the database size. The first DEPIR candidate constructions were recently put forth, based on a new type of assumption relating to indistinguishability of moderate-degree polynomials from random functions when given permuted versions of their evaluation graphs (Boyle, Ishai, Pass, Wootters TCC\u2717 and Canetti, Holmgren, Richelson TCC\u2717). To aid in the cryptanalytic study of this new assumption, the work of (BIPW TCC\u2717) put forth a simpler ``toy conjecture\u27\u27 variant. In this note, we present an attack that provably breaks the BIPW TCC\u2717 toy conjecture. The attack identifies a natural embedding of permuted samples into a higher-dimensional linear space for which permuted polynomial samples will be rank deficient. We note, however, that our attack does not apply to the real assumption underlying the constructions, and thus the candidates still stand. We discuss extensions of the attack and present an alternative ``new toy conjecture\u27\u27 for future study. Similar results were independently obtained by (Blackwell and Wootters, ArXiv\u2721)

Tendon-to-bone enthesis as a structured nanomaterial

Tendon attaches to bone through a hierarchical and spatial graded structure called the enthesis. Entheses at the rotator cuff of the humeral head are highly resilient against injury in younger adults, but tears are common in older adults. These heal poorly, even following surgery. A central challenge is that potentially important nanoscale features of the material at these enthesis sites are not regenerated following injury or surgery. Our group aims to identify the nanoscale structures that are most important to the resilience of the enthesis, and to develop strategies for reconstituting these during healing. Here, we will present an overview of our recent results on ways that both structured and stochastic features might contribute to the mechanical functioning of the healthy enthesis

Rapid transport of muco-inert nanoparticles in cystic fibrosis sputum treated with N -acetyl cysteine

Sputum poses a critical diffusional barrier that strongly limits the efficacy of drug and gene carriers in the airways of individuals with cystic fibrosis (CF). Previous attempts to enhance particle penetration of CF sputum have focused on either reducing its barrier properties via mucolytics, or decreasing particle adhesion to sputum constituents by coating the particle surface with non-mucoadhesive polymers, including polyethylene glycol (PEG). Neither approach has enabled particles to penetrate expectorated sputum at rates previously observed for non-mucoadhesive nanoparticles in human cervicovaginal mucus. Here, we sought to investigate whether a common mucolytic, N-acetyl cysteine (NAC), in combination with dense PEG coatings on particles, can synergistically enhance particle penetration across fresh undiluted CF sputum

Determining the Longissimus lumborum and Psoas major Beef Steak Color Life Threshold and Effect of Postmortem Aging Time Using Meta-analysis

Using meta-analysis, the color life threshold for beef longissimus lumborum (LL) and psoas major (PM) steaks during retail display (phase 1) and the effect of postmortem aging time (phase 2) on the display color life of LL and PM steaks were determined. In phase 1, data were retrieved from 13 refereed journal articles for LL and 3 refereed journal articles for PM, which included a* and subjective visual scores. The total display day observations for LL and PM were 148 and 27, respectively. Lower bound estimates using a 95% confidence interval for a* as a threshold for the display color life of LL and PM steaks were 20.24 and 20.99, respectively. For phase 2, data were retrieved from 26 refereed journal articles for LL and 10 referred journal articles for PM, which included a* and postmortem aging time. The total display day observations for LL and PM in phase 2 were 255 and 71, respectively. For LL steaks, the actual postmortem aging time was grouped into 5 categories: 0–7 d, 8–14 d, 15–21 d, 22–28 d, and 29–65 d. Additionally, the postmortem aging time of PM steaks was grouped into 2 categories: 0–7 d and 8–21 d. The first 21-d postmortem aging time for LL steaks had the longest color life, with 7 d. Additionally, 22 to 28 d of postmortem aging time and 29 to 65 d of postmortem aging time had 5 d and 4 d, respectively, of color life for LL steaks. The borderline acceptability estimated for PM steaks with 0–7 d and 8–21 of postmortem aging time was 3 d and 2 d of color life, respectively. Estimations from this meta-analysis demonstrate that using LL and PM subprimals that have a postmortem aging time of 21 d or less and 7 d or less, respectively, would optimize the retail display color life of aerobically packaged steaks

Nonlinear Effects In Black Hole Ringdown From Scattering Experiments I: spin and initial data dependence of quadratic mode coupling

We investigate quadratic quasinormal mode coupling in black hole spacetime through numerical simulations of single perturbed black holes using both numerical relativity and second-order black hole perturbation theory. Focusing on the dominant $\ell=|m|=2$ quadrupolar modes, we find good agreement (within $\sim10\%$) between these approaches, with discrepancies attributed to truncation error and uncertainties from mode fitting. Our results align with earlier studies extracting the coupling coefficients from select binary black hole merger simulations, showing consistency for the same remnant spins. Notably, the coupling coefficient is insensitive to a diverse range of initial data, including configurations that led to a significant (up to $5\%$) increase in the remnant black hole mass. These findings present opportunities for testing the nonlinear dynamics of general relativity with ground-based gravitational wave observatories. Lastly, we provide evidence of a bifurcation in coupling coefficients between counter-rotating and co-rotating quasinormal modes as black hole spin increases

Imaging of Borrelia turicatae Producing the Green Fluorescent Protein Reveals Persistent Colonization of the Ornithodoros turicata Midgut and Salivary Glands from Nymphal Acquisition through Transmission

Relapsing fever (RF) spirochetes colonize and are transmitted to mammals primarily by Ornithodoros ticks, and little is known regarding the pathogen's life cycle in the vector. To further understand vector colonization and transmission of RF spirochetes, Borrelia turicatae expressing a green fluorescent protein (GFP) marker (B. turicatae-gfp) was generated. The transformants were evaluated during the tick-mammal infectious cycle, from the third nymphal instar to adult stage. B. turicatae-gfp remained viable for at least 18 months in starved fourth-stage nymphal ticks, and the studies indicated that spirochete populations persistently colonized the tick midgut and salivary glands. Our generation of B. turicatae-gfp also revealed that within the salivary glands, spirochetes are localized in the ducts and lumen of acini, and after tick feeding, the tissues remained populated with spirochetes. The B. turicatae-gfp generated in this study is an important tool to further understand and define the mechanisms of vector colonization and transmission. IMPORTANCE In order to interrupt the infectious cycle of tick-borne relapsing fever spirochetes, it is important to enhance our understanding of vector colonization and transmission. Toward this, we generated a strain of Borrelia turicatae that constitutively produced the green fluorescent protein, and we evaluated fluorescing spirochetes during the entire infectious cycle. We determined that the midgut and salivary glands of Ornithodoros turicata ticks maintain the pathogens throughout the vector's life cycle and remain colonized with the spirochetes for at least 18 months. We also determined that the tick's salivary glands were not depleted after a transmission blood feeding. These findings set the framework to further understand the mechanisms of midgut and salivary gland colonization

A forgotten figure in Siouan and Caddoan linguistics: Samuel Stehman Haldeman.

The Siouan family comprises some twenty languages, historically spoken across a broad swath of the central North American plains and woodlands, as well as in parts of the southeastern United States. In spite of its geographical extent and diversity, and the size and importance of several Siouan-speaking tribes, this family has received relatively little attention in the linguistic literature and many of the individual Siouan languages are severely understudied. This volume aims to make work on Siouan languages more broadly available and to encourage deeper investigation of the myriad typological, theoretical, descriptive, and pedagogical issues they raise. The 17 chapters in this volume present a broad range of current Siouan research, focusing on various Siouan languages, from a variety of linguistic perspectives: historical-genetic, philological, applied, descriptive, formal/generative, and comparative/typological. The editors' preface summarizes characteristic features of the Siouan family, including head-final and "verb-centered" syntax, a complex system of verbal affixes including applicatives and subject-possessives, head-internal relative clauses, gendered speech markers, stop-systems including ejectives, and a preference for certain prosodic and phonotactic patterns. The volume is dedicated to the memory of Professor Robert L. Rankin, a towering figure in Siouan linguistics throughout his long career, who passed away in February of 2014

Advances in the study of Siouan languages and linguistics

The Siouan family comprises some twenty languages, historically spoken across a broad swath of the central North American plains and woodlands, as well as in parts of the southeastern United States. In spite of its geographical extent and diversity, and the size and importance of several Siouan-speaking tribes, this family has received relatively little attention in the linguistic literature and many of the individual Siouan languages are severely understudied. This volume aims to make work on Siouan languages more broadly available and to encourage deeper investigation of the myriad typological, theoretical, descriptive, and pedagogical issues they raise. The 17 chapters in this volume present a broad range of current Siouan research, focusing on various Siouan languages, from a variety of linguistic perspectives: historical-genetic, philological, applied, descriptive, formal/generative, and comparative/typological. The editors' preface summarizes characteristic features of the Siouan family, including head-final and "verb-centered" syntax, a complex system of verbal affixes including applicatives and subject-possessives, head-internal relative clauses, gendered speech markers, stop-systems including ejectives, and a preference for certain prosodic and phonotactic patterns. The volume is dedicated to the memory of Professor Robert L. Rankin, a towering figure in Siouan linguistics throughout his long career, who passed away in February of 2014

Advances in the study of Siouan languages and linguistics

The Siouan family comprises some twenty languages, historically spoken across a broad swath of the central North American plains and woodlands, as well as in parts of the southeastern United States. In spite of its geographical extent and diversity, and the size and importance of several Siouan-speaking tribes, this family has received relatively little attention in the linguistic literature and many of the individual Siouan languages are severely understudied. This volume aims to make work on Siouan languages more broadly available and to encourage deeper investigation of the myriad typological, theoretical, descriptive, and pedagogical issues they raise. The 17 chapters in this volume present a broad range of current Siouan research, focusing on various Siouan languages, from a variety of linguistic perspectives: historical-genetic, philological, applied, descriptive, formal/generative, and comparative/typological. The editors' preface summarizes characteristic features of the Siouan family, including head-final and "verb-centered" syntax, a complex system of verbal affixes including applicatives and subject-possessives, head-internal relative clauses, gendered speech markers, stop-systems including ejectives, and a preference for certain prosodic and phonotactic patterns. The volume is dedicated to the memory of Professor Robert L. Rankin, a towering figure in Siouan linguistics throughout his long career, who passed away in February of 2014