Search

In a study of student understanding of negative definite integrals at two institutions, we administered a written survey and follow-up clinical interviews at one institution and found that "backward integrals", where the integral was taken from right to left on the x-axis, were the most difficult for students to interpret. We then conducted additional interviews focused on backward integrals at a second institution. Our analysis uses the concept image framework and a recent categorical framework for mathematical sense making. We found that students were most successful using the Fundamental Theorem of Calculus to determine the sign of an integral when a symbolic expression was provided. When considering a definite integral in a graphical context, students often had difficulty if they viewed the integral as a spatial area, stating that area must always be positive. Some students were able to conceptualize [delta]x or dx as a difference or change and thus a signed quantity; when these students were able to view the area as a sum of smaller pieces, they were more successful in justifying a negative backward integral. Students who used amounts or similar images often had difficulty making sense of the negative sign. Even more progress was made when students either invoked or were asked explicitly about a specific physical context to be represented by the backward integral, other than spatial area. The context provided a meaning to the difference represented by [delta]x or dx and thus to the sign of that difference and the definite integral.

In recent years, there has been an increased interest in conceptual blending in physics and mathematics education research as a theoretical framework to study student reasoning. In this paper, we adapt the conceptual blending framework to construct a blending diagram that not only captures the product but also the process of student reasoning when they interpret a mathematical description of a physical system. We describe how to construct a dynamic blending diagram (DBD) and illustrate this using two cases from an interview study. In the interview, we asked pairs of undergraduate physics and mathematics students about the physical meaning of boundary conditions for the heat equation. The selected examples show different aspects of the DBD as an analysis method. We show that by using a DBD, we can judge the degree to which students integrate their understandings of mathematics and physics. The DBD also enables the reader to follow the line of reasoning of the students. Moreover, a DBD can be used to diagnose difficulties in student reasoning.

Vector calculus and multivariable coordinate systems play a large role in the understanding and calculation of much of the physics in upper-division electricity and magnetism. Differential vector elements represent one key mathematical piece of students' use of vector calculus. In an effort to examine students' understanding of non-Cartesian differential length elements, students in junior-level electricity and magnetism were interviewed in pairs and asked to construct a differential length vector for an unconventional spherical coordinate system. One aspect of this study identified symbolic forms invoked by students when building these vector expressions, some previously identified and some novel, given the vector calculus context. Analysis also highlighted several common ideas in students' concept images of a non-Cartesian differential length vector as they determined their expressions. As no interview initially resulted in the construction of an appropriate differential, analysis addresses the role of the evoked concept images and symbolic forms on students' performance.

How data are collected and how they are analyzed is typically described in the literature, but how the data are encoded is often not described in detail. In this paper, we discuss how data typically gathered in PER are encoded and how the choice of encoding plays a role in data analysis. We describe the kinds of data that are found when using short answer, multiple choice, Likert-scale, ranking task, and free response questions in terms of nominal, ordinal, interval, and ratio data. We discuss the mathematical operations that are available for each kind of data and how this affects ways that similarity and difference between student responses can be determined, a topic we discuss in terms of measures of distances and correlation. Finally, we use several papers from the literature to discuss ways in which data have been encoded and analyzed, with examples of normalized gain, factor analysis, model analysis, cluster analysis, and the investigation of epistemological agreement. We highlight both strengths and weaknesses of the data encoding approaches used in these studies. Our goal is not a comprehensive review, but one that is illustrative and can help researchers understand their own and each other's work more deeply.

Understanding wildfire spread in Canada is critical to promoting forest health and protecting human life and infrastructure. Quantifying fire spread from noisy images, where change-point boundaries separate regions of fire, is critical to accurately estimating fire spread rates. The challenge lies in denoising the fire images and accurately identifying highly non-linear fire lines without smoothing over boundaries. In this paper, we develop an iterative smoothing algorithm for change-point data that utilizes oversmoothed estimates of the underlying data generating process to inform re-smoothing. We demonstrate its effectiveness on simulated one- and two-dimensional change-point data, and robustness to response outliers. Then, we apply the methodology to fire spread images from laboratory micro-fire experiments and show that the regions fuel, burning and burnt-out are smoothed while boundaries are preserved. [ABSTRACT FROM AUTHOR]

The aims of this study were to describe the changes in bone turnover markers (BTMs) in response to lasofoxifene therapy; to describe the changes in BTMs in the individual; and to examine the relationships between BTM levels on treatment and treatment outcomes. Women (n=1126) aged 59-80years with femoral neck or spine bone mineral density T-scores ≤-2.5 were randomized to lasofoxifene 0.25mg/d, 0.5mg/d, or placebo for 5years. We measured serum C-telopeptide of type I collagen (CTX) and serum procollagen I N-propeptide (PINP), osteocalcin, and bone alkaline phosphatase (ALP) at baseline and at 1, 3, 6, 12, 24, and 36months. Lasofoxifene therapy resulted in a decrease in the concentrations of bone resorption and bone formation markers compared with placebo; the decrease was maximal between 6 and 24months. The effect of lasofoxifene 0.5mg/d was similar to that of lasofoxifene 0.25mg/d. The decrease in bone ALP was less than the decreases in CTX, osteocalcin, and PINP. Lasofoxifene therapy 0.5mg/d resulted in BTM-defined response rates for CTX (decrease in concentration from baseline >60%), PINP (>50%), and bone ALP (>30%) of 35%, 45%, and 43% of women at month 12, respectively, compared with placebo responses of 4%, 4%, and 7%. In contrast, the increase in BMD took longer (50% responded after 36months of lasofoxifene 0.5mg/d) and was not as specific (15% of placebo group responded). Bone density change was weakly inversely correlated with change in the concentrations of BTMs. BTMs may prove useful in the monitoring of the response to lasofoxifene treatment for women with postmenopausal osteoporosis early in the course of treatment.

The aims of this study were to describe the changes in bone turnover markers (BTMs) in response to lasofoxifene therapy; to describe the changes in BTMs in the individual; and to examine the relationships between BTM levels on treatment and treatment outcomes. Women (n=1126) aged 59-80years with femoral neck or spine bone mineral density T-scores ≤-2.5 were randomized to lasofoxifene 0.25mg/d, 0.5mg/d, or placebo for 5years. We measured serum C-telopeptide of type I collagen (CTX) and serum procollagen I N-propeptide (PINP), osteocalcin, and bone alkaline phosphatase (ALP) at baseline and at 1, 3, 6, 12, 24, and 36months. Lasofoxifene therapy resulted in a decrease in the concentrations of bone resorption and bone formation markers compared with placebo; the decrease was maximal between 6 and 24months. The effect of lasofoxifene 0.5mg/d was similar to that of lasofoxifene 0.25mg/d. The decrease in bone ALP was less than the decreases in CTX, osteocalcin, and PINP. Lasofoxifene therapy 0.5mg/d resulted in BTM-defined response rates for CTX (decrease in concentration from baseline >60%), PINP (>50%), and bone ALP (>30%) of 35%, 45%, and 43% of women at month 12, respectively, compared with placebo responses of 4%, 4%, and 7%. In contrast, the increase in BMD took longer (50% responded after 36months of lasofoxifene 0.5mg/d) and was not as specific (15% of placebo group responded). Bone density change was weakly inversely correlated with change in the concentrations of BTMs. BTMs may prove useful in the monitoring of the response to lasofoxifene treatment for women with postmenopausal osteoporosis early in the course of treatment.

BackgroundCurrently available selective estrogen receptor modulators reduce the risk of breast cancer, but they are not widely used. In the Postmenopausal Evaluation and Risk-Reduction with Lasofoxifene (PEARL) trial, lasofoxifene was shown to reduce the risk of estrogen receptor-positive (ER+) breast cancer, nonvertebral and vertebral fractures, coronary artery disease, and stroke, but the effects on total breast cancer (invasive and ductal carcinoma in situ, ER+ and estrogen receptor-negative [ER-]) and ER+ invasive breast cancer are unknown.MethodsPostmenopausal women (n = 8556) aged 59-80 years with low bone density and normal mammograms were randomly assigned to two doses of lasofoxifene (0.25 and 0.5 mg) or placebo. The primary endpoints of the PEARL trial were incidence of ER+ breast cancer and nonvertebral fractures at 5 years. A nested case-control study of 49 incident breast cancer case patients and 156 unaffected control subjects from the PEARL trial was performed to evaluate treatment effects on risk of total and ER+ invasive breast cancer by baseline serum estradiol and sex hormone-binding globulin levels using logistic regression models. Cox proportional hazards models were used to evaluate risk of total breast cancer and ER+ invasive breast cancer using intention-to-treat analysis. All statistical tests were two-sided.ResultsBreast cancer was confirmed in 49 women. Compared with placebo, 0.5 mg of lasofoxifene statistically significantly reduced the risk of total breast cancer by 79% (hazard ratio = 0.21; 95% confidence interval [CI] = 0.08 to 0.55) and ER+ invasive breast cancer by 83% (hazard ratio = 0.17; 95% CI = 0.05 to 0.57). The effects of 0.5 mg of lasofoxifene on total breast cancer were similar regardless of Gail score, whereas the effects were markedly stronger for women with baseline estradiol levels greater than the median (odds ratio = 0.11; 95% CI = 0.02 to 0.51) vs those with levels less than the median (odds ratio = 0.78; 95% CI = 0.16 to 3.79; P(interaction) = .04).ConclusionA 0.5-mg dose of lasofoxifene appears to reduce the risks of both total and ER+ invasive breast cancer in postmenopausal women with osteoporosis.

BackgroundIn the Postmenopausal Evaluation and Risk Reduction With Lasofoxifene (PEARL) trial, women assigned to lasofoxifene 0.5 mg/d had a lower risk of major coronary heart disease (CHD) events and stroke, whereas women assigned to lasofoxifene 0.25 mg/d had a lower risk of stroke. Both doses of lasofoxifene increased the risk of venous thromboembolic events. In this report, we provide comprehensive cardiovascular end-point data, including component events comprising the composite end point of major CHD events, and evaluate whether the effect of lasofoxifene 0.5 mg/d is consistent across different categories of CHD risk.Methods and resultsIn this study, 8556 women 59 to 80 years of age with osteoporosis received lasofoxifene 0.25 mg/d, lasofoxifene 0.5 mg/d, or placebo for 5 years. Cardiovascular events, including major CHD events, were prespecified secondary end points. Compared with placebo, lasofoxifene 0.5 mg/d reduced the risk of major CHD events 32% (hazard ratio, 0.68; 95% confidence interval, 0.50 to 0.93), including the risk of coronary revascularization (hazard ratio, 0.56, 95% confidence interval, 0.32 to 0.98). Reductions in risk of hospitalization for unstable angina (hazard ratio, 0.55; 95% confidence interval, 0.29 to 1.04) and diagnosis of new ischemic heart disease (hazard ratio, 0.52; 95% confidence interval, 0.26 to 1.04) nearly reached significance (P=0.06 for both comparisons). Although both hazard ratios were

Plasma concentrations of total cholesterol, low-density lipoprotein cholesterol, high-density lipoprotein cholesterol and triglycerides are among the most important risk factors for coronary artery disease (CAD) and are targets for therapeutic intervention. We screened the genome for common variants associated with plasma lipids in >100,000 individuals of European ancestry. Here we report 95 significantly associated loci (P < 5 x 10(-8)), with 59 showing genome-wide significant association with lipid traits for the first time. The newly reported associations include single nucleotide polymorphisms (SNPs) near known lipid regulators (for example, CYP7A1, NPC1L1 and SCARB1) as well as in scores of loci not previously implicated in lipoprotein metabolism. The 95 loci contribute not only to normal variation in lipid traits but also to extreme lipid phenotypes and have an impact on lipid traits in three non-European populations (East Asians, South Asians and African Americans). Our results identify several novel loci associated with plasma lipids that are also associated with CAD. Finally, we validated three of the novel genes-GALNT2, PPP1R3B and TTC39B-with experiments in mouse models. Taken together, our findings provide the foundation to develop a broader biological understanding of lipoprotein metabolism and to identify new therapeutic opportunities for the prevention of CAD.

Problem solving, which often involves multiple steps, is an integral part of physics learning and teaching. Using the perspective of the epistemic game, we documented a specific game that is commonly pursued by students while solving mathematically based physics problems: the "analytical derivation" game. This game involves deriving an equation through symbolic manipulations and routine mathematical operations, usually without any physical interpretation of the processes. This game often creates cognitive obstacles in students, preventing them from using alternative resources or better approaches during problem solving. We conducted hour-long, semi-structured, individual interviews with fourteen introductory physics students. Students were asked to solve four "pseudophysics" problems containing algebraic and graphical representations. The problems required the application of the fundamental theorem of calculus (FTC), which is one of the most frequently used mathematical concepts in physics problem solving. We show that the "analytical derivation" game is necessary, but not sufficient, to solve mathematically based physics problems, specifically those involving graphical representations.

New compounds and coordination polymers with highly polarizable metals (M = Hg, Pb) and 2,2';6'2'-terpyridine (terpy) and 2,6-bis(benzimidazol-2-yl)pyridine (bbp) ligands have been synthesized and characterized for their photo-physical and optical properties. Hg(L)[(CN).sub.2] (L = terpy, bbp) exhibit [pi]-stacking interactions, which form a supramolecular alignment of the planar terpy and bbp units. Pb(terpy)[X.sub.2][[Hg[(CN).sub.2]].sub.0.5] (X = Cl, Br) generate one-dimensional coordination polymers through bridging Hg[(CN).sub.2] linkers and hydrogen-bonding interactions. All of the metal centres have very distorted coordination geometries. Hg(L)[(CN).sub.2] (L = terpy, bbp) and Pb(terpy)[Br.sub.2][[Hg[(CN).sub.2]].sub.0.5] show terpy or bbp based emission. The materials are very birefringent, with [DELTA]n ranging from 0.37(2) to 0.45(2). The magnitude of the observed birefringence depends on the orientation of the highly polarizable terpy and bbp units in relation to the viewing axis of the crystals. These materials represent rare examples of multifunctional emissive and birefringent systems. Key words: coordination polymer, cyanide, terpyridine, bis(benzimidazol-2-yl)pyridine, stereochemically active lone pair. Nous avons synthetise de nouveaux composes et polymeres de coordination contenant des metaux hautement polarisables (M = Hg, Pb) et les ligands 2,2';6'2'-terpyridine (terpy) et 2,6-bis(benzimidazol-2-yl)pyridine (bbp), et nous les avons caracterises selon leurs proprietes photophysiques et optiques. Les complexes Hg(L)[(CN).sub.2] (L = terpy, bbp) presentent des interactions p-p qui donnent lieu a un alignement supramoleculaire des motifs planaires terpy et bbp. Les complexes Pb(terpy)[X.sub.2] [[Hg[(CN).sub.2]].sub.0.5] (X = Cl, Br) generent des polymeres de coordination en 1D maintenus par des ponts Hg[(CN).sub.2] et des liaisons hydrogene. Tous les centres metalliques possedent une geometrie de coordination tres deformee. Les complexes Hg(L)[(CN).sub.2] (L = terpy, bbp) et Pb(terpy)[Br.sub.2][[Hg[(CN).sub.2]].sub.0.5] manifestent une capacite d'emission attribuable aux ligands terpy et bbp. Ces composes sont tres birefringents, leur An allant de 0,37(2) a 0,45(2). L'ampleur de la birefringence observee depend de l'orientation des unites tres polarisables terpy et bbp par rapport a l'axe de visualisation des cristaux. Ces composes font partie des rares exemples de systemes multifonctionnels emissifs et birefringents. [Traduit par la Redaction] Mots-cles : polymere de coordination, cyanure, terpyridine, bis(benzimidazol-2-yl)pyridine, doublet non liant stereochimiquement reactif., Introduction Coordination polymers are metal-ligand networks that extend in one, two, or three dimensions and are formed through coordination bonds between metal nodes and linker units. (1,2) The structural geometries [...]

A series of octahedral [Co.sup.III] salen complexes (where salen represents a [N.sub.2][O.sub.2] bis-Schiff-base bis-phenolate framework) were prepared with axial imidazole ligating groups. When using 1-methylimidazole (1-MeIm) axial ligands, the [Co.sup.III]/[Co.dup.II] reduction potential could be altered by 220 mV via variation of the electron-donating ability of the para-ring substituents (R = H(1), OMe (2), tBu (3), Br (4), N[O.sub.2] (5), and C[F.sub.3] (6)). In addition, the irreversibility of the reduction process suggested substantial geometrical changes and axial ligand exchange upon reduction to the more labile [Co.sup.II] oxidation state. Installing an imidazole-coumarin conjugate as the axial ligands resulted in fluorescence quenching when bound to the [Co.sup.III] centre (R = H(7), OMe (8), and C[F.sub.3] (9)). The redox properties and fluorescence increase upon ligand release for 7-9 were studied under reducing conditions and in the presence of excess competing ligand (1-MeIm). It was determined that the Lewis acidity of the [Co.sup.III] centre was the dominant factor in controlling axial ligand exchange for this series of complexes. Key words: cobalt, cancer, hypoxia, reduction, ligand exchange. Nous avons synthetise une serie de complexes de [Co.sup.III] salen octaedriques (ou salen represente un ligand bis-phenolate-bis-base de Schiff a coordination de type [N.sub.2][O.sub.2]) coordonnes a des groupements axiaux a base d'imidazole. Lorsque nous avons employe des ligands axiaux a base de 1-methylimidazole (1-MeIm), le potentiel de reduction du [Co.sup.III] en [Co.sup.II] pouvait varier de 220 mV selon la capacite des substituants en position para sur le noyau aromatique [R = H(1), OMe (2), tBu (3), Br (4), N[O.sub.2] (5)et C[F.sub.3] (6)] a donner des electrons. De plus, le fait que la reduction etait irreversible semble indiquer que des changements geometriques substantiels et un echange de ligands axiaux se sont produits lors de la reduction du cobalt vers l'etat d'oxydation plus labile ([Co.sup.II]). L'ajout d'un conjugue de type imidazole-coumarine comme ligands axiaux s'est traduit par une extinction de la fluorescence au moment de sa liaison a l'atome central de [Co.sup.III] [R = H(7), OMe (8)etC[F.sub.3] (9)]. Nous avons etudie les proprietes d'oxydoreduction et l'amplification de la fluorescence des composes 7 a 9 lorsque le ligand est libere en conditions reductrices et en presence d'un exces du ligand en competition (1-MeIm). Nous avons etabli que, dans cette serie de complexes, l'acidite de Lewis de l'atome central de [Co.sup.III] etait le facteur determinant dans l'echange de ligands. [Traduit par la Redaction] Mots-cles: cobalt, cancer, hypoxie, reduction, echange de ligands., Introduction There is an increasing interest in metal-based drugs for diagnostic and therapeutic applications, due to the need to increase both potency and selectivity (.1-5) The ability to vary the [...]

We present results of our investigation into student understanding of the physical significance and utility of the Boltzmann factor in several simple models. We identify various justifications, both correct and incorrect, that students use when answering written questions that require application of the Boltzmann factor. Results from written data as well as teaching interviews suggest that many students can neither recognize situations in which the Boltzmann factor is applicable nor articulate the physical significance of the Boltzmann factor as an expression for multiplicity, a fundamental quantity of statistical mechanics. The specific student difficulties seen in the written data led us to develop a guided-inquiry tutorial activity, centered around the derivation of the Boltzmann factor, for use in undergraduate statistical mechanics courses. We report on the development process of our tutorial, including data from teaching interviews and classroom observations of student discussions about the Boltzmann factor and its derivation during the tutorial development process. This additional information informed modifications that improved students' abilities to complete the tutorial during the allowed class time without sacrificing the effectiveness as we have measured it. These data also show an increase in students' appreciation of the origin and significance of the Boltzmann factor during the student discussions. Our findings provide evidence that working in groups to better understand the physical origins of the canonical probability distribution helps students gain a better understanding of when the Boltzmann factor is applicable and how to use it appropriately in answering relevant questions. [This paper is part of the Focused Collection on Upper Division Physics Courses.]

We report on several specific student difficulties regarding the second law of thermodynamics in the context of heat engines within upper-division undergraduate thermal physics courses. Data come from ungraded written surveys, graded homework assignments, and videotaped classroom observations of tutorial activities. Written data show that students in these courses do not clearly articulate the connection between the Carnot cycle and the second law after lecture instruction. This result is consistent both within and across student populations. Observation data provide evidence for myriad difficulties related to entropy and heat engines, including students' struggles in reasoning about situations that are physically impossible and failures to differentiate between differential and net changes of state properties of a system. Results herein may be seen as the application of previously documented difficulties in the context of heat engines, but others are novel and emphasize the subtle and complex nature of cyclic processes and heat engines, which are central to the teaching and learning of thermodynamics and its applications. Moreover, the sophistication of these difficulties is indicative of the more advanced thinking required of students at the upper division, whose developing knowledge and understanding give rise to questions and struggles that are inaccessible to novices. [This paper is part of the Focused Collection on Upper Division Physics Courses.]