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DiPaolo, M. (2021) Fake Italian: An 83% True Autobiography with Pseudonyms and Some Tall Tales. Bordighera Press
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Inertia Sets of Semicliqued Graphs
No full textIn this paper, we investigate inertia sets of simple connected undirected graphs. The main focus is on the shape of their corresponding inertia tables, in particular whether or not they are trapezoidal. This paper introduces a special family of graphs created from any given graph, , coined semicliqued graphs and denoted . We establish the minimum rank and inertia sets of some in relation to the original graph . For special classes of graphs, , it can be shown that the inertia set of is a subset of the inertia set of . We provide the inertia sets for semicliqued cycles, paths, stars, complete graphs, and for a class of trees. In addition, we establish an inertia set bound for semicliqued complete bipartite graphs
Generalized Standard Triples for Algebraic Linearizations of Matrix Polynomials
No full textWe define generalized standard triples , , and , where is a linearization of a regular matrix polynomial , in order to use the representation which holds except when is an eigenvalue of . This representation can be used in constructing so-called algebraic linearizations for matrix polynomials of the form from generalized standard triples of and . This can be done even if and are expressed in differing polynomial bases. Our main theorem is that can be expressed using the coefficients of the expression in terms of the relevant polynomial basis. For convenience, we tabulate generalized standard triples for orthogonal polynomial bases, the monomial basis, and Newton interpolational bases; for the Bernstein basis; for Lagrange interpolational bases; and for Hermite interpolational bases
What’s Worth Knowing? Research and Instructional Impacts of Books on Working-Class Academics
No full textWhat are the research impacts and instructional impacts of books of essays on the perspectives of faculty from working-class backgrounds? To what extent are these books used in undergraduate or graduate courses? Previous research on the content of these edited volumes has been limited to manual constant comparative analyses that described book content. This study employed data analysis methods in the emerging field of altmetric sciences to investigate the impacts of books of personal essays about faculty from working-class backgrounds (N=11). Book-level and chapter-level analyses were conducted to measure research impact using the Altmetric Explorer online tool and instructional impact using the Open Syllabus Project Explorer online tool. Data analysis results on research impacts for books on working-class academics produced extremely low impact levels. Few books (N=4) generated patterns of attention and these patterns were limited in scope. Data analysis results on instructional impacts identified that each of the 11 books generated a Teaching Score, but all scores were minimal and indicated low impact levels. The results suggest that scholarship on faculty from working-class social origins is not being widely included in undergraduate or graduate course syllabi. Further, a large proportion of the book-level scholarship in the subject area of ‘faculty diversity’ has been limited to the constructs of race and gender. Issues involving faculty social origins have been largely omitted from curricula in this area and raises the important question: What is worth knowing
McAlevey, J. (2016) No Shortcuts: Organizing for Power in the New Gilded Age; Oxford University Press.
No full textDivergent Approaches to Access: How Selective College Admissions Offices Recruit Lower-Income, First-Generation, and Working-Class Students
No full textIn recent years, selective colleges and universities have made diversifying their student bodies a top priority, yet the class diversity on these campuses has barely shifted. While most research on class disparities in college admissions focuses on student explanations, this study seeks to understand how campus admissions approaches to recruitment may also contribute to why so few lower-income, first-generation, and/or working-class students (LIFGWC students) attend selective colleges. To address this question, we conducted interviews with seven admissions officers from selective campuses with both relatively strong and weak records of LIFGWC students recruitment. Institutions with stronger records of recruiting LIFGWC students actively sought out new initiatives to make their college more accessible for LIFGWC students, and these actions were motivated by a shared focus on improving larger societal inequality. Although campuses with weaker records also expanded their recruitment strategies, their efforts were often piecemeal and motivated by competition for students and institutional rankings rather than a larger mission to improve diversity and equity. These findings suggest that institutional missions and philosophies are central to increasing access.
 
Improvements on Spectral Bisection
No full textIn this paper, the third eigenvalue of the Laplacian matrix is used to provide a lower bound on the minimum cutsize. This result has algorithmic implications that are exploited in this paper. Besides, combinatorial properties of certain configurations of a graph partition which are related to the minimality of a cut are investigated. It is shown that such configurations are related to the third eigenvector of the Laplacian matrix. It is well known that the second eigenvector encodes structural information, and that can be used to approximate a minimum bisection. In this paper, it is shown that the third eigenvector carries structural information as well. Then a new spectral bisection algorithm using both eigenvectors is provided. The new algorithm is guaranteed to return a cut that is smaller or equal to the one returned by the classic spectral bisection. Also, a spectral algorithm that can refine a given partition and produce a smaller cut is provided
m-commuting maps on triangular and strictly triangular infinite matrices
No full textLet be the ring of infinite strictly upper triangular matrices with entries in an infinite field. The description of the commuting maps defined on , i.e. the maps such that for every , is presented. With the use of this result, the form of -commuting maps defined on -- the ring of infinite upper triangular matrices, i.e. the maps such that for every , is found