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Agriculture ranks one of the top contributors to global warming and nutrient pollution. Quantifying life cycle environmental impacts from agricultural production serves as scientific foundation for forming effective remediation strategies. However, the methods capable of accurately and efficiently calculating spatially explicit life cycle global warming and eutrophication impacts at a fine spatial scale over a geographic region are lacking. The objective of this study was to compare two regression models for estimating spatially explicit life cycle global warming and eutrophication, with corn production in the Midwest region as a demonstrating example. The results indicated that the gradient boosting regression tree model built with monthly weather features yielded higher predictive accuracy for life cycle global warming impact and life cycle EU. Moreover, predictive accuracy was improved at the cost of simulation time. The gradient boosting regression tree model required longer training time. Additionally, all machine learning models were million times faster than the traditional process-based model and were suitable for use in computationally-intensive applications like optimization and predication. © 2019 IEEE.

Freshwater unionid mussels produce a bilayered shell with the mineral proportion comprising an outer prismatic and an inner nacreous layer. The shell is the animals’ primary structural means of protection from predators and environmental challenges; therefore, variations in shell strength and properties may lead to differences in survival. Few studies have systematically assessed shell properties in unionids. A major challenge in such work is separating effects of environment from those of evolutionary history, because ultimately, both can affect shell properties. We collected eight species of unionids within a small area of the Allegheny River, Pennsylvania, that was relatively homogeneous in substratum type and other environmental characteristics. For each species, we quantified shell thickness, including thickness of the prismatic and nacreous layers, and shell micromechanical properties (microhardness and crack propagation, a measure of fracture resistance) in three regions of the shell. Shell thickness varied dramatically among species and was about five times greater in the thickest-shelled species, Pleurobema sintoxia, than in the thinnest-shelled species, Villosa iris. Because all species experienced similar environmental conditions, variation in shell thickness can be attributed largely to evolutionary history. In contrast, microhardness and crack propagation showed little variation among species. Given that micromechanical properties are similar among species, shell strength may be largely a function of thickness. These results have conservation implications, as differences in shell thickness could reflect relative vulnerability to predators and physical conditions

The purpose of this study is to investigate secondary teacher candidates’ experience of mathematical modeling task design. In the study, 54 teacher candidates in a university-based teacher education program created modeling tasks and scoring rubrics. Next, the participants pilot-tested the tasks with students and had the opportunity to revise the original tasks and rubrics based on student responses. The data included participants’ statements, in which they described and reflected on the design and revision process of modeling tasks. The study describes six didactic revision strategies in revising modeling tasks and identifies five emerging pedagogical ideas from revising tasks and rubrics. The study also discusses the way modeling task design activities have the potential to support teacher candidates’ learning through a bottom-up modeling curriculum in teacher education.

Wide field planetary camera 2 (WFPC2) exposures are already some 20 years older than Gaia epoch observations, or future James Webb Space Telescope observations. As such, they offer an unprecedented time baseline for high-precision proper-motion studies, provided the full astrometric potential of these exposures is reached. We have started such a project with the work presented here being its first step. We explore geometric distortions beyond the well-known ones published in the early 2000 s. This task is accomplished by using the entire database of WFPC2 exposures in filters F555W, F606W and F814W and three standard astrometric catalogs: Gaia EDR3, 47 Tuc and ωCen. The latter two were constructed using Hubble Space Telescope observations made with cameras other than WFPC2. We explore a suite of centering algorithms, and various distortion maps in order to understand and quantify their performance. We find no high-frequency systematics beyond the 34th-row correction, down to a resolution of 10 pixels. Low-frequency systematics starting at a resolution of 50 pixels are present at a level of 30–50 millipix (1.4–2.3 mas) for the PC and 20–30 millipix (2–3 mas) for the WF chips. We characterize these low-frequency systematics by providing correction maps and updated cubic-distortion coefficients for each filter.

An (a, b)-Sudoku pair Latin square is a Latin square that is simult-aneously an (a, b)-Sudoku Latin square and a (b, a)-Sudoku Latin square. While (a, b)-Sudoku Latin squares are known to exist for any positive integers a and b, the pairs a, b for which an (a, b)-Sudoku pair Latin square exists are largely unknown. In this article we establish the existence of (a, b)-Sudoku pair Latin squares for an infinite collection of pairs (a, b). Our results show that a (3, b)-Sudoku pair Latin square can be constructed for any positive integer b. ©The author(s).

This study investigates how pre-service teachers use their knowledge of technology, mathematics, and pedagogy to create video lessons using portable interactive whiteboards. The TPACK framework was used to identify the different types of knowledge pre-service teachers rely on as they create their videos. Results indicate pre-service teachers’ effective use of conveyance technology, pedagogical techniques, and mathematical representations using technology. Their videos portray their process of coordinating their TPACK. Recommendations are made for teacher educators to integrate technology in activities that aim to develop pre-service teachers’ comfort and confidence with technological tools for teaching and learning. © 2021 ATE and CCNY.

Background: Attenuation correction (AC) using CT transmission scanning enables the accurate quantitative analysis of dedicated cardiac SPECT. However, AC is challenging for SPECT-only scanners. We developed a deep learning-based approach to generate synthetic AC images from SPECT images without AC. Methods: CT-free AC was implemented using our customized Dual Squeeze-and-Excitation Residual Dense Network (DuRDN). 172 anonymized clinical hybrid SPECT/CT stress/rest myocardial perfusion studies were used in training, validation, and testing. Additional body mass index (BMI), gender, and scatter-window information were encoded as channel-wise input to further improve the network performance. Results: Quantitative and qualitative analysis based on image voxels and 17-segment polar map showed the potential of our approach to generate consistent SPECT AC images. Our customized DuRDN showed superior performance to conventional network design such as U-Net. The averaged voxel-wise normalized mean square error (NMSE) between the predicted AC images by DuRDN and the ground-truth AC images was 2.01 ± 1.01%, as compared to 2.23 ± 1.20% by U-Net. Conclusions: Our customized DuRDN facilitates dedicated cardiac SPECT AC without CT scanning. DuRDN can efficiently incorporate additional patient information and may achieve better performance compared to conventional U-Net. © 2021, American Society of Nuclear Cardiology.

A Skolem sequence can be thought of as a labelled path where two vertices with the samelabelarethatdistanceapart.Thisconcepthasnaturallybeengeneralizedto labellingsofothergraphs,butalwaysusingatmosttwoofanyintegerlabel.Giventhat more than two vertices can be mutually distance d apart, wedefine a new generalization of aSkolemsequenceongraphsthatwecallaproperSkolemlabelling.Thisbrings rise tothequestion;use to proper Skolemlabel a graph?"This will be known as the Skolem number of the graph. In this paper we give the Skolem number for cycles and grid graphs,while also providing other related results along the way. Published by Digital Commons@Georgia Southern, 2021. © 2021 Georgia Southern University. All rights reserved.

A rokudoku-pair square is an order-6 sudoku Latin square for both 2 x 3 and 3 x 2 tiling regions simultaneously. We count the distinct rokudoku-pair squares as well as orbits under the action of a suitable group. Our arguments employ group actions and list colorings of graphs. As an application we determine which rokudoku-pair squares are based on groups. © 2021. All Rights Reserved.

This paper will discuss the correlation between the SAT and the Math Inventory Test. Many school districts adopted the Math Inventory as a tool to measure student growth from grades kindergarten through high school. The Math Inventory is a computer-administered test that gives students math problems spanning from counting to high school level math. When completed, the students are given a quantile measure, much like a Lexile score for reading skill. The purpose of this study is to figure out if success on the Math Inventory is a good indicator for performing well on the SAT. For most high schools around the United States, objectives and lessons are aligned with those of the SAT. The goal of high school teachers is for students to excel on the SAT so that they can go to college, which means the tests used in middle school should be aligned with that goal. If the Math Inventory is not, then it might not be a very good use of school time and resources. Data was analyzed from the 2017-2018 school year from ten different high schools in an urban school district to determine the correlation between Math Inventory score, and the math score/sub scores of SAT/PSAT. The value of the Pearson’s correlation coefficient is used to suggest a fairly moderate positive relationship between these two variables. © 2021, International Journal of Information and Education Technology. All rights reserved.

The increasing number of technological devices available in schools, aligned with curriculum guidance, set an expectation for mathematics teachers to incorporate these devices into their teaching. This qualitative study investigated prospective teachers’ use of TPACK and mathematical action technologies as they created screencast video lessons using iPads. Results showed prospective teachers’ effective use of pedagogical techniques and the screencast app as an amplifier tool, according to the amplifier-reorganizer metaphor. Half of the participants used mathematics technology to confirm and expand the results they had found without technology. The other half had mathematics technology integrated into their solution exercising the balance among TPACK components. For some, their use of the mathematical tool had the potential of expanding the mathematical repertoire of virtual students. We conclude by making recommendations for teacher educators to implement cycles of learning for pre-service teachers to design, enact, and reflect upon the creation of screencast video lessons. © 2021, Association for Educational Communications & Technology.

Agriculture ranks as one of the top contributors to global warming and nutrient pollution. Quantifying life cycle environmental impacts from agricultural production serves as a scientific foundation for forming effective remediation strategies. However, methods capable of accurately and efficiently calculating spatially explicit life cycle global warming (GW) and eutrophication (EU) impacts at the county scale over a geographic region are lacking. The objective of this study was to determine the most efficient and accurate model for estimating spatially explicit life cycle GW and EU impacts at the county scale, with corn production in the U.S.’s Midwest region as a case study. This study compared the predictive accuracies and efficiencies of five distinct supervised machine learning (ML) algorithms, testing various sample sizes and feature selections. The results indicated that the gradient boosting regression tree model built with approximately 4000 records of monthly weather features yielded the highest predictive accuracy with cross-validation (CV) values of 0.8 for the life cycle GW impacts. The gradient boosting regression tree model built with nearly 6000 records of monthly weather features showed the highest predictive accuracy with CV values of 0.87 for the life cycle EU impacts based on all modeling scenarios. Moreover, predictive accuracy was improved at the cost of simulation time. The gradient boosting regression tree model required the longest training time. ML algorithms demonstrated to be one million times faster than the traditional process-based model with high predictive accuracy. This indicates that ML can serve as an alternative surrogate of process-based models to estimate life-cycle environmental impacts, capturing large geographic areas and timeframes.

Consider a finite t + r − 1 dimensional projective space PG(t + r − 1, s) over a Galois field GF(s) of order s = ϱh, where ϱ and h are positive integers and ϱ is the prime characteristic of the field. A collection of k points in PG (t + r − 1, s) constitutes an L(t, k)-set if no t of them are linearly dependent. An L(t, k)-set is maximal if there exists no other L(t, k′)-set with k′ > k. The largest k for which an L(t, k)-set exists is denoted by Mt(t + r, s). K. A. Bush [3] established that Mt(t, s) = t + 1 for t ⩾ s. The purpose of this paper is to generalize this result and study Mt(t + r, s) for t, r, and s in certain relationships.

Consider a finite (t + r - 1)-dimensional projective space PG(t + r - 1, s) based on the Galois field GF(s), where s is prime or power of a prime. A set of k distinct points in PG(t + r - 1, s), no t-linearly dependent, is called a (k, t)-set and such a set is said to be maximal if it is not contained in any other (k*, t)-set with k* > k. The number of points in a maximal (k, t)-set with the largest k is denoted by mt(t + r, s). Our purpose in the paper is to investigate the conditions under which two or more points can be adjoined to the basic set of Ei, i = 1, 2, ..., t + r, where Ei is a point with one in i-th position and zeros elsewhere. The problem has several applications in the theory of fractionally replicated designs and information theory. © 1973.

Consider a finite r-dimensional projective space PG(r, s) based on the Galois field GF(s) where s is prime or power of a prime. A set of n distinct points in PG(r, s), no t linearly dependent, is said to be maximal or complete if it is not contained in any other set with n* points with n* > n. The number of points in a maximal set is denoted by mt(r + 1, s). The purpose of this paper is to improve the existing bounds for m5(r + 1, s) for r ≥ 5 and s ≥ 5 (odd). The investigation of maximal sets in certain relationships of t, r and s yields parity check matrices of (r + 1) rows and n columns with elements from GF(s) satisfying the condition that no t columns are linearly dependent. This problem has applications to coding theory and also in the theory of fractionally replicated designs. © 1972 Academic Press, Inc.

This investigation was originally motivated by the problem of determining the maximum number of points in finite n-dimensional projective space PG(n, s) based on the Galois field GF(s) of order s=ph (where p and h are positive integers and p is the prime characteristic of the field), such that no t of these chosen points are linearly dependent. A set of k distinct points in PG(n, s), no t linearly dependent, is called a (k, t)-set for k1 >k. The maximum value of k is denoted by mt (n+1, s). The purpose of this paper is to find new upper bounds for some values of n, s and t. These bounds are of importance in the experimental design and information theory problems. © 1971 Institute of Statistical Mathematics.