Applying Graph Theory to Examine the Dynamics of Student Discussions in Small-Group Learning.

Group work in science, technology, engineering, and mathematics courses is an effective means of improving student outcomes, and many different factors can influence the dynamics of student discussions and, ultimately, the success of collaboration. The substance and dynamics of group discussions are commonly examined using qualitative methods such as discourse analysis. To complement existing work in the literature, we developed a quantitative methodology that uses graph theory to map the progression of talk-turns of discussions within a group. We observed groups of students working with peer facilitators to solve problems in biological sciences, with three iterations of data collection and two major refinements of graph theory calculations. Results include general behaviors based on the turns in which different individuals talk and graph theory parameters to quantify group characteristics. To demonstrate the potential utility of the methodology, we present case studies with distinct patterns: a centralized group in which the peer facilitator behaves like an authority figure, a decentralized group in which most students talk their fair share of turns, and a larger group with subgroups that have implications for equity, diversity, and inclusion. Together, these results demonstrate that our adaptation of graph theory is a viable quantitative methodology to examine group discussions

Numerical investigation of the Rayleigh hypothesis for electromagnetic scattering by a particle

The validity of the Rayleigh hypothesis has been a long-standing issue in the applicability of the T-matrix method to near-field calculations, and despite numerous theoretical works, the practical consequences for numerical simulations have remained unclear. Such calculations are increasingly important in the field of nanooptics, for which accurate and efficient modeling tools are in high demand. We here tackle this challenge by investigating numerically the convergence behavior of series expansions of the electric field around spheroidal particles, which provides us with unambiguous examples to clarify the conditions of convergence. This study is made possible by the combination of alternative methods to compute near-fields accurately, and crucially, the recent improvements in the calculation of T-matrix elements free from numerical instabilities, as such errors would otherwise obfuscate the intrinsic convergence properties of the field series. The resulting numerical confirmation for the range of validity of the Rayleigh hypothesis, complemented by a better understanding of the convergence behavior of the field expansions, is a crucial step toward future developments

Regional surname affinity: a spatial network approach

OBJECTIVE We investigate surname affinities among areas of modern‐day China, by constructing a spatial network, and making community detection. It reports a geographical genealogy of the Chinese population that is result of population origins, historical migrations, and societal evolutions. MATERIALS AND METHODS We acquire data from the census records supplied by China's National Citizen Identity Information System, including the surname and regional information of 1.28 billion registered Chinese citizens. We propose a multilayer minimum spanning tree (MMST) to construct a spatial network based on the matrix of isonymic distances, which is often used to characterize the dissimilarity of surname structure among areas. We use the fast unfolding algorithm to detect network communities. RESULTS We obtain a 10‐layer MMST network of 362 prefecture nodes and 3,610 edges derived from the matrix of the Euclidean distances among these areas. These prefectures are divided into eight groups in the spatial network via community detection. We measure the partition by comparing the inter‐distances and intra‐distances of the communities and obtain meaningful regional ethnicity classification. DISCUSSION The visualization of the resulting communities on the map indicates that the prefectures in the same community are usually geographically adjacent. The formation of this partition is influenced by geographical factors, historic migrations, trade and economic factors, as well as isolation of culture and language. The MMST algorithm proves to be effective in geo‐genealogy and ethnicity classification for it retains essential information about surname affinity and highlights the geographical consanguinity of the population.National Natural Science Foundation of China, Grant/Award Numbers: 61773069, 71731002; National Social Science Foundation of China, Grant/Award Number: 14BSH024; Foundation of China of China Scholarships Council, Grant/Award Numbers: 201606045048, 201706040188, 201706040015; DOE, Grant/Award Number: DE-AC07-05Id14517; DTRA, Grant/Award Number: HDTRA1-14-1-0017; NSF, Grant/Award Numbers: CHE-1213217, CMMI-1125290, PHY-1505000 (61773069 - National Natural Science Foundation of China; 71731002 - National Natural Science Foundation of China; 14BSH024 - National Social Science Foundation of China; 201606045048 - Foundation of China of China Scholarships Council; 201706040188 - Foundation of China of China Scholarships Council; 201706040015 - Foundation of China of China Scholarships Council; DE-AC07-05Id14517 - DOE; HDTRA1-14-1-0017 - DTRA; CHE-1213217 - NSF; CMMI-1125290 - NSF; PHY-1505000 - NSF)Published versio

High-Temperature Series Analyses of the Classical Heisenberg and XY Model

Although there is now a good measure of agreement between Monte Carlo and high-temperature series expansion estimates for Ising ($n=1$) models, published results for the critical temperature from series expansions up to 12{\em th} order for the three-dimensional classical Heisenberg ($n=3$) and XY ($n=2$) model do not agree very well with recent high-precision Monte Carlo estimates. In order to clarify this discrepancy we have analyzed extended high-temperature series expansions of the susceptibility, the second correlation moment, and the second field derivative of the susceptibility, which have been derived a few years ago by L\"uscher and Weisz for general $O(n)$ vector spin models on $D$-dimensional hypercubic lattices up to 14{\em th} order in $K \equiv J/k_B T$. By analyzing these series expansions in three dimensions with two different methods that allow for confluent correction terms, we obtain good agreement with the standard field theory exponent estimates and with the critical temperature estimates from the new high-precision MC simulations. Furthermore, for the Heisenberg model we reanalyze existing series for the susceptibility on the BCC lattice up to 11{\em th} order and on the FCC lattice up to 12{\em th} order.Comment: 15 pages, Latex, 2 PS figures not included. FUB-HEP 18/92 and HLRZ 76/9

Tidal instability in a rotating and differentially heated ellipsoidal shell

The stability of a rotating flow in a triaxial ellipsoidal shell with an imposed temperature difference between inner and outer boundaries is studied numerically. We demonstrate that (i) a stable temperature field encourages the tidal instability, (ii) the tidal instability can grow on a convective flow, which confirms its relevance to geo- and astrophysical contexts and (iii) its growth rate decreases when the intensity of convection increases. Simple scaling laws characterizing the evolution of the heat flux based on a competition between viscous and thermal boundary layers are derived analytically and verified numerically. Our results confirm that thermal and tidal effects have to be simultaneously taken into account when studying geophysical and astrophysical flows

Tubulin cofactors and Arl2 are cage-like chaperones that regulate the soluble αβ-tubulin pool for microtubule dynamics.

Microtubule dynamics and polarity stem from the polymerization of αβ-tubulin heterodimers. Five conserved tubulin cofactors/chaperones and the Arl2 GTPase regulate α- and β-tubulin assembly into heterodimers and maintain the soluble tubulin pool in the cytoplasm, but their physical mechanisms are unknown. Here, we reconstitute a core tubulin chaperone consisting of tubulin cofactors TBCD, TBCE, and Arl2, and reveal a cage-like structure for regulating αβ-tubulin. Biochemical assays and electron microscopy structures of multiple intermediates show the sequential binding of αβ-tubulin dimer followed by tubulin cofactor TBCC onto this chaperone, forming a ternary complex in which Arl2 GTP hydrolysis is activated to alter αβ-tubulin conformation. A GTP-state locked Arl2 mutant inhibits ternary complex dissociation in vitro and causes severe defects in microtubule dynamics in vivo. Our studies suggest a revised paradigm for tubulin cofactors and Arl2 functions as a catalytic chaperone that regulates soluble αβ-tubulin assembly and maintenance to support microtubule dynamics

The biHecke monoid of a finite Coxeter group and its representations

For any finite Coxeter group W, we introduce two new objects: its cutting poset and its biHecke monoid. The cutting poset, constructed using a generalization of the notion of blocks in permutation matrices, almost forms a lattice on W. The construction of the biHecke monoid relies on the usual combinatorial model for the 0-Hecke algebra H_0(W), that is, for the symmetric group, the algebra (or monoid) generated by the elementary bubble sort operators. The authors previously introduced the Hecke group algebra, constructed as the algebra generated simultaneously by the bubble sort and antisort operators, and described its representation theory. In this paper, we consider instead the monoid generated by these operators. We prove that it admits |W| simple and projective modules. In order to construct the simple modules, we introduce for each w in W a combinatorial module T_w whose support is the interval [1,w]_R in right weak order. This module yields an algebra, whose representation theory generalizes that of the Hecke group algebra, with the combinatorics of descents replaced by that of blocks and of the cutting poset.Comment: v2: Added complete description of the rank 2 case (Section 7.3) and improved proof of Proposition 7.5. v3: Final version (typo fixes, picture improvements) 66 pages, 9 figures Algebra and Number Theory, 2013. arXiv admin note: text overlap with arXiv:1108.4379 by other author

Critical adsorption at chemically structured substrates

We consider binary liquid mixtures near their critical consolute points and exposed to geometrically flat but chemically structured substrates. The chemical contrast between the various substrate structures amounts to opposite local preferences for the two species of the binary liquid mixtures. Order parameters profiles are calculated for a chemical step, for a single chemical stripe, and for a periodic stripe pattern. The order parameter distributions exhibit frustration across the chemical steps which heals upon approaching the bulk. The corresponding spatial variation of the order parameter and its dependence on temperature are governed by universal scaling functions which we calculate within mean field theory. These scaling functions also determine the universal behavior of the excess adsorption relative to suitably chosen reference systems

New Baryons in the Delta eta and Delta omega Channels

The decays of excited nonstrange baryons into the final states Delta eta and Delta omega are examined in a relativized quark pair creation model. The wavefunctions and parameters of the model are fixed by previous calculations of N pi and N pi pi, etc., decays through various quasi-two body channels including N eta and N omega. Our results show that the combination of thresholds just below the region of interest and the isospin selectivity of these channels should allow the discovery of several new baryons in such experiments.Comment: 10 pages, RevTe

UNLV College of Education Multicultural & Diversity Newsletter

Each morning I wound my way up the steep hill along the deeply rutted dirt path, exchanging daily maaa\u27s with five bleating sheep and shouting out, ¡Hola! in response to the children who gleefully identified me as ¡Gringa! Women and children, colorful bowls of cooked maize balanced atop their heads, sauntered to and from Maria Elena\u27s where their maize would be ground; at home the dough would be shaped and flattened into tortillas, the mainstay of every meal in the small Guatemalan village of San Juan