Search Results - Mathematics of computing Discrete mathematics Graph theory Graph enumeration

List of Publications of Ivo G. Rosenberg.

Source: Journal of Multiple-Valued Logic & Soft Computing; 2025, Vol. 44 Issue 5/6, p601-621, 21p

Subject Terms: DISCRETE mathematics, COMBINATORICS, MATHEMATICAL logic, GRAPH theory, ORDERED algebraic structures, TRIANGLES

Extraction of exact symbolic stationary probability formulas for Markov chains with finite space with application to production lines. Part I: description of methodology.

Authors: Boulas, Konstantinos S. Dounias, Georgios D. Papadopoulos, Chrissoleon T.

Source: Frontiers in Manufacturing Technology; 2025, p1-17, 17p

Subject Terms: MARKOV processes, GRAPH theory, STOCHASTIC matrices, ASYMPTOTIC distribution, QUEUING theory, SPANNING trees, ANALYTICAL solutions

Teaching and learning discrete mathematics.

Authors: Sandefur, James Lockwood, Elise Hart, Eric et al.

Source: ZDM - Mathematics Education; Aug2022, Vol. 54 Issue 4, p753-775, 23p

Subject Terms: GRAPH theory, MATHEMATICS education, NUMBER theory, POSTSECONDARY education, GAME theory

Geographic Terms: CHILE

Algorithms and Data Structures for First-Order Logic with Connectivity Under Vertex Failures

Authors: Pilipczuk, Michał Schirrmacher, Nicole Siebertz, Sebastian et al.

Contributors: Pilipczuk, Michał Schirrmacher, Nicole Siebertz, Sebastian et al.

Subject Terms: FOS: Computer and information sciences, Computer Science - Logic in Computer Science, Data structures, Discrete Mathematics (cs.DM), Mathematics of computing → Graph algorithms, Fixed-parameter algorithms and complexity, Mathematics - Logic, 0102 computer and information sciences, Theory of computation → Finite Model Theory, 01 natural sciences, Logic in Computer Science (cs.LO), Theory of computation → Fixed parameter tractability, Computational applications of logic, Computer Science - Data Structures and Algorithms, Combinatorics and graph theory, FOS: Mathematics, Mathematics - Combinatorics, Data Structures and Algorithms (cs.DS), Combinatorics (math.CO), ddc:004, Logic (math.LO), Graph algorithms, Computer Science - Discrete Mathematics

File Description: application/pdf

Access URL: http://arxiv.org/abs/2111.03725
https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2022.102

On Entropy of Some Fractal Structures.

Authors: Ghazwani, Haleemah Nadeem, Muhammad Faisal Ishfaq, Faiza et al.

Source: Fractal & Fractional; May2023, Vol. 7 Issue 5, p378, 23p

Subject Terms: UNCERTAINTY (Information theory), MULTIFRACTALS, ENTROPY, DISTRIBUTION (Probability theory), GRAPH theory, COMPUTATIONAL mathematics

Geographic Terms: ZAGREB (Croatia)

Graph and Network Theory

Authors: Michael A. Henning Jan H. van Vuuren

Resource Type: eBook.

Subjects: Graph theory

Categories: BUSINESS & ECONOMICS / Operations Research, BUSINESS & ECONOMICS / Management Science, MATHEMATICS / Discrete Mathematics

Graphs for Pattern Recognition : Infeasible Systems of Linear Inequalities

Authors: Damir Gainanov

Resource Type: eBook.

Subjects: Inequalities (Mathematics), Graph theory

Categories: MATHEMATICS / Combinatorics, COMPUTERS / Image Processing, COMPUTERS / Programming / Algorithms, MATHEMATICS / Applied, MATHEMATICS / Geometry / General, MATHEMATICS / Optimization

Approximate sampling and counting of graphs with near-regular degree intervals

Authors: Amanatidis, Georgios Kleer, Pieter

Source: SIAM Journal on Discrete Mathematics vol.38 (2024) nr.4 p.2812-2840 [ISSN 0895-4801]

Index Terms: Degree intervals, Graph sampling, switch Markov chain, Article

URL: https://research.tilburguniversity.edu/en/publications/3a958ee5-d387-4936-9f37-e87a8518216c
https://repository.tilburguniversity.edu/bitstreams/f08c064f-52df-4c1c-8985-1ea0f7f11279/download
https://repository.tilburguniversity.edu/bitstreams/f08c064f-52df-4c1c-8985-1ea0f7f11279/download

Maximal Planar Graph Theory and the Four-Color Conjecture

Authors: Jin Xu

Resource Type: eBook.

Subjects: Graph coloring, Geometry

Categories: COMPUTERS / Computer Science

THE DISCRETE YET UBIQUITOUS THEOREMS OF CARATHÚEODORY, HELLY, SPERNER, TUCKER, AND TVERBERG.

Authors: DE LOERA, JESÚUS A. GOAOC, XAVIER MEUNIER, FRÚEDÚERIC et al.

Source: Bulletin (New Series) of the American Mathematical Society; Jul2019, Vol. 56 Issue 3, p415-511, 97p

Subject Terms: GRAPH theory, COMBINATORIAL geometry, MATHEMATICAL optimization, COMPUTATIONAL geometry, COMPUTATIONAL mathematics

Enumeration of loopless maps on the projective plane

Authors: Yanpei Liu Zhaoxiang Li

Source: Journal of Applied Mathematics and Computing. 10:145-155

Subject Terms: enumerating function, 0102 computer and information sciences, 0101 mathematics, Enumeration in graph theory, asymptotic estimate, 01 natural sciences, Planar graphs, geometric and topological aspects of graph theory

File Description: application/xml

Access URL: https://link.springer.com/article/10.1007/BF02936213
https://link.springer.com/content/pdf/10.1007/BF02936213.pdf

Computing Dense and Sparse Subgraphs of Weakly Closed Graphs: Computing dense and sparse subgraphs of weakly closed graphs

Authors: Tomohiro Koana Christian Komusiewicz Frank Sommer et al.

Contributors: Tomohiro Koana Christian Komusiewicz Frank Sommer et al.

Source: Algorithmica. 85:2156-2187

Subject Terms: FOS: Computer and information sciences, Discrete Mathematics (cs.DM), 500 Naturwissenschaften und Mathematik::510 Mathematik::510 Mathematik, dominating set, 0102 computer and information sciences, c-closure, 01 natural sciences, Graph theory, clique relaxations, bicliques, \(c\)-closure, Fixed-parameter tractability, fixed-parameter tractability, c-Closure, FOS: Mathematics, degeneracy, Mathematics - Combinatorics, Combinatorics (math.CO), ddc:004, Algorithms in computer science, Computer Science - Discrete Mathematics

File Description: application/xml; application/pdf

Access URL: http://arxiv.org/abs/2007.05630
https://zbmath.org/7704072
https://doi.org/10.1007/s00453-022-01090-z
https://drops.dagstuhl.de/opus/volltexte/2020/13364/
https://dblp.uni-trier.de/db/journals/corr/corr2007.html#abs-2007-05630
https://drops.dagstuhl.de/opus/volltexte/2020/13364/pdf/LIPIcs-ISAAC-2020-20.pdf/
https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2020.20

Retracted

Authors: Fathi, Kevin

Subject Terms: Quantum Gravity, Compact Generation, Spectral Correspondence, Asymptotic Analysis, Supercuspidal Representations, Automorphic representations, Halting Problem, Local Quantum Gradient Descent, Compression Theory, Number Theory, Compression-based unprovability, Mathematical Logic, Canonical Grammars, Canonical Normal Form, Galois Parameters in Mod- ℓ, recursive sequences, Frame Coherence, Symbolic entropy, Moduli Spaces, Trace Functor, Delta-Based Routing, Dark Energy, Riemann Hypothesis, Rational Points on Varieties, Double bind logic, Symbolic Irreducibility, Strategic Ambiguity, Quantum Kolmogorov complexity, Endoscopic Character Identities, sequence coverage, Dynamic Network Relabeling, growth lemma, Quantum complexity theory, Rewrite Grammars, Trace Pairing, Automorphic L-functions, Combinatorial Number Theory, Spectral Trace Rigidity, Constructive logic, Graph Labeling, Millennium Prize Problems, Statistical Mechanics, Vacuum Spectrum, Theoretical computer science, Representation-Theoretic Stability, Trace Operator, k-Local Hamiltonian, Mod- ℓ Transfer Factors, Torsion Sheaves, Scalable Network Protocols, Entropy Saturation, Purity Theorem, Shannon Entropy, Moy–Prasad Filtration, Algorithmic Information Theory, Shimura Varieties, Resolve budget, Information-theoretic logic, Ramsey Theory, Computability Theory, natural number shuffles, Distributed Systems, combinatorics, Boltzmann Entropy, Canonical CNF grammar, Vacuum Structure, Rational Hodge Classes, insertion-deletion systems, Witness Incompressibility Conjecture (WIC), Residue Class Elimination, Trace Formula, Symbolic Entropy, Energy Extraction, Reflective Frame Logic (RFL), Algebraic Cycles, Recursive Geometry, Rational Points, Non-Stoquastic Hamiltonian, Complexity Theory, Extremal Set Theory, Representation Theory over Finite Fields, d-regular expander, Computational Irreversibility, Obstruction Theory, Clause Complexity, Lattice-Confined Deuterium, Spectral Geometry, Frobenius and Inertia Actions, Chaitin's Omega, Recursive grammar, Functoriality, Motives, Diophantine Equations, Thermodynamics, Quantum Computing, Satake Parameters, Topological Energy Fields, Epsilon Factors, Indicator Vectors, S-Duality, Mordell–Weil Rank, Langlands Functoriality, Peano Arithmetic, Zero-Point Energy, Ramified Mod- ℓ Types, Cohomological Realization, Parity constraints, Sieve Methods, Rational points, Monoidal Duality, integer permutation, Navier–Stokes, Shafarevich–Tate Group, Mod- ℓ Representation Theory, Algebraic cycles, Frame coherence, Quantum Control, Clause Saturation, Budget-Incompressibility Conjecture (BIC), Spectral Functor, Combinatorics, Tseitin formulas, Derived Category, Graph Theory, Derived Categories, Arithmetic Geometry, Eigenvalue Symmetry, Canonical Normal Forms, Meta-mathematics, Structural Compression, Extremal Combinatorics, Fine-Structure Constant, Twin Primes, Stable Distributions, Cohomology theory, Unified Physics, Mod- ℓ Langlands, Resolution proof complexity, Symbolic Central Limit Theorem, computational complexity, Physical Computation, Symbolic Irreversibility, Computational complexity, Trace dynamics, Density Bounds, Graceful Tree Conjecture, Recursive Type Arithmetic, Foundations of Mathematics, Landauer's Principle, Cycle Class Map, Hecke Algebras over 𝐹 ℓ, monotonic insertion, Formal grammar, Reductive p-adic Groups, sequence generalization, FOS: Mathematics, Stable Character Identities, p-adic Langlands, Mirror Symmetry, Learning systems, Automorphic Representations, Ergodic Symbolic Processes, Spectral Trace, Irreducibility, Time-Bounded Quantum-to-Classical Principle, Fixpoint Dynamics, Incompressibility, Global Functoriality, combinatorial construction, Entropy-bound derivation, Symbolic Probability, Canonical Functorial Lift, Mass Gap, Local Modularity Lifting, Brane Categories, Quantum Boon-Bind Hierarchy (QBBH), Langlands functoriality, Spectral gap, Canonical rewrite systems, Graceful Labeling, Mod- ℓ Langlands Program, Elementary Methods, Frame Topos Theory (FTT), Condensed Matter Fusion, Langlands Endoscopy, Algorithmic information theory, Kimberling sequence, Trace Stabilization, Pseudo-L-Groups, Prime Constellations, Network Topology Verification, Mathematical Physics, Symbolic compression, Harish-Chandra Expansion, Spectral Gap, Admissible Sets, Asymptotic Enumeration, Dualizability, Trace Rigidity, Curvature Quantization, Roth's Theorem, Gravitational Curvature, Path Trace Encoding, Quantum BindTseitin Hamiltonian, Information-Theoretic Physics, ∞-Categories, Symbolic Dynamics, Symbolic Trace Compression, Probabilistic Limit Theorems, Frame Collapse, Turing reduction, Quantum Field Theory, Additive Combinatorics, Degeneracy, Information theory, Trace Cohomology, Étale Cohomology, Symbolic collapse, Langlands Duality, Recursive Labeling, Quantum Coherence, k-Tuple Conjecture, Temporal Cosmology, Canonical Bijection, Pigeonhole Principle, Frobenius Trace, Discrete Mathematics, Inductive Graph Theory, Positivity of Trace, Computability theory, Galois Parameters, Grammar-Based Inference, Algebraic geometry, Nonlinear Dynamics, P vs NP problem, Tame vs Wild Representations, Epsilon Factors in Mod- ℓ Setting, Mathematical logic, Kolmogorov Complexity, Topos Theory, Wild Ramification, Evolutionary selection, Parity Hamiltonian, Statistical mechanics, Algebraic Geometry, Modular Forms, Quantum Boon-Bind Hierarchy, structural complexity, Non-Gaussian Limit Laws, Hilbert Space Geometry, Trace Operators, Eigenvarieties, Unified symbolic theorem, Wild Supercuspidals, Black Hole Information, Quantum Langlands, Entropy Gradient, Bateson Game, Address Collision Avoidance, Landauer principle, Structural Paradox, P vs NP, Yang–Mills Theory, Sheaf Theory, Analytic rank, Base Change in Mod- ℓ Setting, Prime Distribution, Frobenius and Inertia Types, Arithmetic Progressions, Langlands Classification in Characteristic ℓ, Foundations of Computation, Computational complexity theory, Residue Coverage, rewrite systems, Feynman–Kitaev Hamiltonian, Tame vs Wild Modularity, Modular Obstruction, Elementary Number Theory, Stable Trace Formula, Gauge Theory, Endomorphism Algebra, BindTseitin constraints, Tree-Based Networks, Cohomological Descent, Structural Complexity, Foundational mathematics, Hodge classes, Entropy gradient, Entropy-based inference, Quantum Vacuum, Formal Language Theory, Budget-Incompressibility Conjecture, symbolic dynamics, XOR-SAT, Structural Bounds, Mod- l Local Langlands, Harish-Chandra Characters, proof by contradiction, Elliptic Curves, Unbounded Prime Gaps, Quantum State Coherence, Representation Theory, Parameter Lifting, growth argument, Galois Representations, PDE Curvature, Automorphic Representations mod- ℓ, Busy Beaver Function, CNF formulas, Mod- ℓ Galois Parameter, Batesonian Physics, Proof Theory, Reduction of ℓ-adic Representations, Algorithmic Randomness, Turing Machines, Tannakian Categories, Kolmogorov complexity, Network Addressing, Fusion Reaction Pathways, Twisted D-Modules, Sign Problem, Tseitin transformation, Langlands Correspondence, Selmer group, Local Langlands Correspondence, Structural irreversibility, Spectral Decomposition, History state, Edge Difference Encoding, Quantum Kolmogorov Complexity, Functional Equation, Convergence and fixation, Character Expansion, NP-completeness, Automorphic Sheaves, Edge Difference Uniqueness, Synergy, Meta-logic, Growth Barrier, Wild Inertial Types, CNF Grammar, Orbital Integrals, fixpoint collapse, One-way functions, Variable Progression Length, Formal logic, Universal Equivalence, Energy barriers, Path Integral Methods, Hecke Eigensheaves, Forbidden Configurations, symbolic grammar, L-group homomorphisms, Character Theory, Non-Reductive Groups, coverage theorem, double bind machine, integer sequences, Overlap Gap Property, Quantum Tunneling, Tamagawa Numbers, Regulator, Progression-Free Sets, Beal Conjecture, k-local Hamiltonian, Reductive Groups over Global Fields, Fixpoint Descent, Erdős Problems, natural number permutation, Frame compression barrier, Entropy-Based Convergence, Routing Algorithms, Yang–Mills Mass Gap, Universal Frame Logic (UFL), Mod- ℓ L-functions, Wireless Sensor Networks, Information Theory, Derived Stacks, Birch and Swinnerton-Dyer Conjecture, number theory, Elliptic curves, Frustrated Quantum Systems, Post-ZFC Logic, semantic degeneracy, recursive enumeration, Perverse Sheaves, L-packets and Character Matching, Entropy-based proof, L-packets and Stability, Prime Patterns, Gauge Symmetry, Epistemic foundations of math, Categorical Proof, Recursive Structures, Geometric Langlands, Recursive Type Arithmetic (RTA), Chaitin incompleteness, Geometric Langlands with Torsion Coefficients, Reductive Groups, Character Matching, Symbolic proof systems, Prime Tuples, Edge expansion, Entropy–complexity correspondence, Theoretical Computer Science, logical paradox, Clause Overlap, Ecological Physics, Spectral Kernel, Hodge Theory, Injective Labeling, Mod- ℓ Langlands Correspondence, Recursive Logic, algorithmic information theory, Mod- ℓ Shimura Varietie, Entropy Production, Meta-Coherence Logic (MCL), Motivic Cohomology, Structural paradox, Endoscopic Transfer, Encoding asymmetry, Unified Field Theory, Szemerédi's Theorem, Fixpoint Rigidity, Categorical Trace, Modularity Lifting, Global Fields, symbolic entropy, Entropy Geometry, Entropy Collapse, Label-Delta Matching, L-functions, Depth-Positive Types, Langlands Dual Group, Configuration Entropy, Recursive Frame Theory, Quantum Complexity Theory, Time Emergence, Muon-Catalyzed Fusion, Additive Number Theory, Mod- ℓ Eigenvarieties, Mod- ℓ Trace Formula, Spectral Rigidity, Batesonian Game Theory, Positive Energy, Hodge Conjecture, Behrend Construction, Canonical CNF encoding, Prime Factorization, Constructive Algorithms, constructive proof, elementary proof, Moduli Stacks, Cryptographic hardness, Low-Energy Nuclear Fusion, BQP vs. QMA, one-way function, Modular Representation Theory, Mod- ℓ Local Langlands, Density Threshold, Tree Structures, Depth Stratification, Tunneling Probability, Noncomputability, Entropy collapse, Automorphic L-Functions, Incompleteness theorem, ∞-Categorical Descent, BB(6), Hardy–Littlewood Conjecture, Bit Complexity Optimization, Graph Theory Applications, Proof theory, Derived Moduli Stacks, Langlands Program, Recursive Tension Fields, Szemerédi-Type Theorems, Expander graphs, Frobenius Trace Invariants, Inertial Equivalence, Multicast Routing, Arithmetic Moduli, Millennium Problems

Subgraph densities in a surface

Authors: Huynh, T. Joret, G. Wood, D. R.

Source: Combinatorics, Probability and Computing. 31:812-839

Subject Terms: graph embedding, FOS: Computer and information sciences, Extremal problems in graph theory, Discrete Mathematics (cs.DM), homomorphism inequality, Graph minors, 0102 computer and information sciences, graph, Enumeration in graph theory, 01 natural sciences, Planar graphs, geometric and topological aspects of graph theory, FOS: Mathematics, Théorie des graphes, surface, Mathematics - Combinatorics, Graphs, Surfaces, Extremal Graph Theory, Combinatorics (math.CO), 0101 mathematics, Paths and cycles, Computer Science - Discrete Mathematics

File Description: application/xml; 1 full-text file(s): application/pdf

Access URL: http://arxiv.org/pdf/2003.13777
http://arxiv.org/abs/2003.13777
https://zbmath.org/7671081
https://doi.org/10.1017/s0963548321000560
https://hdl.handle.net/11573/1705861

Coloured Tutte polynomials and Kauffman brackets for graphs of bounded tree width

Authors: J. A. Makowsky

Source: Discrete Applied Mathematics. 145:276-290

Subject Terms: Tutte polynomial, Coloring of graphs and hypergraphs, Knot polynomials, Graph algorithms (graph-theoretic aspects), Graph theory (including graph drawing) in computer science, Applied Mathematics, Discrete Mathematics and Combinatorics, 0102 computer and information sciences, Combinatorial enumeration, 0101 mathematics, Combinatorial aspects of matroids and geometric lattices, Fixed parameter complexity, 01 natural sciences

File Description: application/xml

Access URL: https://dl.acm.org/doi/10.5555/365411.365514
https://dblp.uni-trier.de/db/conf/soda/soda2001.html#Makowsky01

On computing boundary functional sums

Authors: A. A. Sapozhenko

Source: Discrete Mathematics. 213:253-260

Subject Terms: boundary functional, Independent set, Expander, Exact enumeration problems, generating functions, independent sets number, matchings number, 0102 computer and information sciences, 01 natural sciences, enumeration, Theoretical Computer Science, Graph theory, Boundary functional, percolation problem, binary codes number, Discrete Mathematics and Combinatorics, 0101 mathematics

File Description: application/xml

Access URL: https://www.sciencedirect.com/science/article/pii/S0012365X99001855
https://www.sciencedirect.com/science/article/abs/pii/S0012365X99001855
https://doi.org/10.1016/S0012-365X(99)00185-5

Local multiple alignment via subgraph enumeration

Authors: B. He Z. Zhang Webb Miller

Source: Discrete Applied Mathematics. 71:337-365

Subject Terms: 0301 basic medicine, Extremal problems in graph theory, sequence comparison, Multiple alignment, Biochemistry, molecular biology, chaining, Applied Mathematics, Applications of graph theory, blocking, 0102 computer and information sciences, Enumeration in graph theory, 01 natural sciences, Sequence comparison, Subgraph enumeration, flattening, 03 medical and health sciences, maximal clique, Graph theory (including graph drawing) in computer science, subgraph enumeration, molecular biology, Discrete Mathematics and Combinatorics, Maximal clique, Computational methods for problems pertaining to biology, Software, source code, etc. for problems pertaining to biology, multiple alignments

File Description: application/xml

Access URL: https://zbmath.org/981930
https://doi.org/10.1016/s0166-218x(96)00072-8
https://www.sciencedirect.com/science/article/pii/S0166218X96000728
https://dblp.uni-trier.de/db/journals/dam/dam71.html#ZhangHM96
https://www.sciencedirect.com/science/article/abs/pii/S0166218X96000728

Finding parity difference by involutions

Authors: Grzegorz Stachowiak

Source: Discrete Mathematics. 163:139-151

Subject Terms: Permutations, words, matrices, Eulerian and Hamiltonian graphs, multiset permutation, Combinatorics on words, Analysis of algorithms and problem complexity, Exact enumeration problems, generating functions, minimal change generating algorithm, colour classes, Combinatorics in computer science, 0102 computer and information sciences, 02 engineering and technology, Enumeration in graph theory, hamitonian path, 01 natural sciences, Trees, Theoretical Computer Science, Combinatorics of partially ordered sets, generation algorithm, minimal change graph, 0202 electrical engineering, electronic engineering, information engineering, Discrete Mathematics and Combinatorics, linear extensions of posets, generation of trees, combinatorial objects

File Description: application/xml

Access URL: https://dblp.uni-trier.de/db/journals/dm/dm163.html#Stachowiak97
http://www.sciencedirect.com/science/article/pii/0012365X9500339X
https://doi.org/10.1016/0012-365X(95)00339-X
https://www.sciencedirect.com/science/article/pii/0012365X9500339X
https://www.sciencedirect.com/science/article/abs/pii/0012365X9500339X

The chromatic polynomial of an unlabeled graph

Authors: Philip J. Hanlon

Source: Journal of Combinatorial Theory, Series B. 38:226-239

Subject Terms: acyclic orientations, counting unlabeled acyclic digraphs, Directed graphs (digraphs), tournaments, chromatic polynomial, 0102 computer and information sciences, Enumeration in graph theory, 01 natural sciences, Theoretical Computer Science, Coloring of graphs and hypergraphs, Computational Theory and Mathematics, cycle index sum equations, Discrete Mathematics and Combinatorics, 0101 mathematics, unlabeled graph

File Description: application/xml

Access URL: https://dblp.uni-trier.de/db/journals/jct/jctb38.html#Hanlon85
https://core.ac.uk/display/82579124
http://www.sciencedirect.com/science/article/pii/0095895685900681
https://www.sciencedirect.com/science/article/pii/0095895685900681

Omega Indices of Strong and Lexicographic Products of Graphs.

Authors: Huilgol MI D'Souza GD Cangul IN

Source: Current organic synthesis [Curr Org Synth] 2025; Vol. 22 (2), pp. 143-158.

Publication Type: Journal Article

Journal Info: Publisher: Bentham Science Publishers Country of Publication: United Arab Emirates NLM ID: 101208457 Publication Model: Print Cited Medium: Internet ISSN: 1570-1794 (Print) Linking ISSN: 15701794 NLM ISO Abbreviation: Curr Org Synth Subsets: PubMed not MEDLINE; MEDLINE