The structure matrix of the class of r-multigraphs with a prescribed degree sequence

AbstractWe introduce a structure matrix Sr(D) into the study of the class Gr(D) of r-multigraphs with the prescribed degree sequence D. Our structure matrix plays the role of the one used by Ryser, Fulkerson, and others to investigate classes of matrices of 0's and 1's with prescribed row and column sums. We develop a theory that is wholly analogous to the classical one. We show that under a type of monotonicity assupmtion on D=(d1,…,dn) the class Gr(D) is nonempty if and only if the sum d1+⋯+dn is even and thr structure matrix Sr(D) is nonnegative. We also prove a generalization of the analogue of ryser's maximum term rank fromula. This result includes both a formula for the maximum number of edges in a matching and a formula for the maximumnumber of edges in a spanning nearly regular subgraph among all graphs with a prescribed degree sequence

Sphericity, cubicity, and edge clique covers of graphs

AbstractThe sphericity sph(G) of a graph G is the minimum dimension d for which G is the intersection graph of a family of congruent spheres in Rd. The edge clique cover number θ(G) is the minimum cardinality of a set of cliques (complete subgraphs) that covers all edges of G. We prove that if G has at least one edge, then sph(G)⩽θ(G). Our upper bound remains valid for intersection graphs defined by balls in the Lp-norm for 1⩽p⩽∞

Trades in complex Hadamard matrices

A trade in a complex Hadamard matrix is a set of entries which can be changed to obtain a different complex Hadamard matrix. We show that in a real Hadamard matrix of order $n$ all trades contain at least $n$ entries. We call a trade rectangular if it consists of a submatrix that can be multiplied by some scalar $c \neq 1$ to obtain another complex Hadamard matrix. We give a characterisation of rectangular trades in complex Hadamard matrices of order $n$ and show that they all contain at least $n$ entries. We conjecture that all trades in complex Hadamard matrices contain at least $n$ entries.Comment: 9 pages, no figure

Hospital Analytics Adoption: Determinants of Choice and Performance Impacts

Technology investment in the healthcare industry has targeted both transaction support systems, such as Electronic MedicalRecords (EMR), and decision support technologies, such as clinical data warehouses and data mining software. While EMRtechnology adoption has received considerable attention in research studies, decision support technology adoptiondeterminants have received less attention. This study aims to investigate the determinants of adoption of decision analyticssystems in hospitals and the resulting impact on hospital performance. Using the Heckman selection model (to correct fordiscrete strategic decision-making endogeneity) on a cross-sectional and representative set of U.S. hospitals integrated fromvarious data sources, we examine the determinants of choice and resulting quality performance impacts of adopting clinicalanalytics systems. We find that EMR systems implementations are good predictors of clinical analytics systems adoption. Wealso find that the performance impacts of process enabled EMR systems are partially influenced by adoption of analyticssoftware

Early Adoption of Patient Portals by U.S. Hospitals

Customer-facing information systems have received very little research attention, especially in the context of healthcare. Ashospitals begin to provide healthcare consumers with online patient portals to view and manage personal health records anddiagnostic results, little is known about whether or not the ‘dominant paradigm’ (Fichman 2004) of diffusion of innovationstheory is sufficient for explaining the characteristics of early adopters. We suggest that a more nuanced understanding ofearly adoption of patient portals is needed because early adopters are not only the largest hospitals with substantial resourcesand capabilities residing within competitive environments. Specifically, we suggest that patient-portals are impacted bymarket characteristics and require Electronic Medical Records (EMRs) systems to be adopted first. We develop a non-linear,two-stage, econometric model with sample selection correction that controls for EMR adoption and estimates the impact ofdiffusion of innovation and market characteristics on the early adoption of patient portals by U.S. hospitals

Simple Analyses of the Sparse Johnson-Lindenstrauss Transform

For every n-point subset X of Euclidean space and target distortion 1+eps for 0l_2^m where f(x) = Ax for A a matrix with m rows where (1) m = O((log n)/eps^2), and (2) each column of A is sparse, having only O(eps m) non-zero entries. Though the constructions given for such A in (Kane, Nelson, J. ACM 2014) are simple, the analyses are not, employing intricate combinatorial arguments. We here give two simple alternative proofs of their main result, involving no delicate combinatorics. One of these proofs has already been tested pedagogically, requiring slightly under forty minutes by the third author at a casual pace to cover all details in a blackboard course lecture

Uniform Maine Citations, 2019 - 2020 Edition (Superseded)

Uniform Maine Citations is organized so that similar types of references to Maine authorities appear together. The organization is grouped by primary or secondary research materials, including subdivisions for (1) statutory and legislative materials, including constitutions, statutes, legislative documents, and municipal ordinances; (2) court decisions, rules, and documents; (3) executive agency regulations, reports, and other documents; and (4) secondary materials that analyze and interpret the primary materials, including Maine-specific treatises, practice books, and legal periodicals. Beyond guidance for proper citation, the primary and secondary sources identified in this edition constitute a useful catalog of materials available to support research into Maine legal authority and sources that discuss them. Further, Uniform Maine Citations identifies the major law libraries and the state and federal court and state government websites that provide free access to primary sources for Maine-specific legal research materials. Maine Uniform Citations undertakes to provide annually updated guidance for the proper form for citation to and location of Maine-specific primary and secondary legal source material. As with the editions that most recently preceded it, this edition is published on the University of Maine School of Law website alongside the Maine Law Review page and is updated at least annually on the academic calendar to recognize new developments and new sources of Maine-related legal research.https://digitalcommons.mainelaw.maine.edu/uniform-maine-citations/1015/thumbnail.jp

Uniform Maine Citations, 2022-2024 Edition

Uniform Maine Citations is organized so that similar types of references to Maine authorities appear together. The organization is grouped by primary or secondary research materials, including subdivisions for (1) statutory and legislative materials, including constitutions, statutes, legislative documents, and municipal ordinances; (2) court decisions, rules, and documents; (3) executive agency regulations, reports, and other documents; and (4) secondary materials that analyze and interpret the primary materials, including Maine-specific treatises, practice books, and legal periodicals. Beyond guidance for proper citation, the primary and secondary sources identified in this edition constitute a useful catalog of materials available to support research into Maine legal authority and sources that discuss them. Further, Uniform Maine Citations identifies the major law libraries and the state and federal court and state government websites that provide free access to primary sources for Maine-specific legal research materials. Maine Uniform Citations undertakes to provide annually updated guidance for the proper form for citation to and location of Maine-specific primary and secondary legal source material. As with the editions that most recently preceded it, this edition is published on the University of Maine School of Law website alongside the Maine Law Review page and is updated at least annually on the academic calendar to recognize new developments and new sources of Maine-related legal research.https://digitalcommons.mainelaw.maine.edu/uniform-maine-citations/1018/thumbnail.jp

Uniform Maine Citations, 2020 - 2021 Edition (Superseded)

Uniform Maine Citations is organized so that similar types of references to Maine authorities appear together. The organization is grouped by primary or secondary research materials, including subdivisions for (1) statutory and legislative materials, including constitutions, statutes, legislative documents, and municipal ordinances; (2) court decisions, rules, and documents; (3) executive agency regulations, reports, and other documents; and (4) secondary materials that analyze and interpret the primary materials, including Maine-specific treatises, practice books, and legal periodicals. Beyond guidance for proper citation, the primary and secondary sources identified in this edition constitute a useful catalog of materials available to support research into Maine legal authority and sources that discuss them. Further, Uniform Maine Citations identifies the major law libraries and the state and federal court and state government websites that provide free access to primary sources for Maine-specific legal research materials. Maine Uniform Citations undertakes to provide annually updated guidance for the proper form for citation to and location of Maine-specific primary and secondary legal source material. As with the editions that most recently preceded it, this edition is published on the University of Maine School of Law website alongside the Maine Law Review page and is updated at least annually on the academic calendar to recognize new developments and new sources of Maine-related legal research.https://digitalcommons.mainelaw.maine.edu/uniform-maine-citations/1016/thumbnail.jp

Uniform Maine Citations, 2021 - 2022 Edition

Uniform Maine Citations is organized so that similar types of references to Maine authorities appear together. The organization is grouped by primary or secondary research materials, including subdivisions for (1) statutory and legislative materials, including constitutions, statutes, legislative documents, and municipal ordinances; (2) court decisions, rules, and documents; (3) executive agency regulations, reports, and other documents; and (4) secondary materials that analyze and interpret the primary materials, including Maine-specific treatises, practice books, and legal periodicals. Beyond guidance for proper citation, the primary and secondary sources identified in this edition constitute a useful catalog of materials available to support research into Maine legal authority and sources that discuss them. Further, Uniform Maine Citations identifies the major law libraries and the state and federal court and state government websites that provide free access to primary sources for Maine-specific legal research materials. Maine Uniform Citations undertakes to provide annually updated guidance for the proper form for citation to and location of Maine-specific primary and secondary legal source material. As with the editions that most recently preceded it, this edition is published on the University of Maine School of Law website alongside the Maine Law Review page and is updated at least annually on the academic calendar to recognize new developments and new sources of Maine-related legal research.https://digitalcommons.mainelaw.maine.edu/uniform-maine-citations/1017/thumbnail.jp