Theoretical Computer Science, ISSN 0304-3975, 01/2017, Volume 658, pp. 190 - 204

Two words and are -abelian equivalent if for each word of length at most , occurs equally many times as a factor in both and . The notion of -abelian...

Hamiltonian paths | Necklaces | Gray codes | de Bruijn graph | k-abelian equivalence | COMPUTER SCIENCE, THEORY & METHODS | Jewelry | Lower bounds | Equivalence | Upper bounds | Alphabets | Binary codes | Graphs | Decomposition | Joints | Computer Science | Discrete Mathematics

Hamiltonian paths | Necklaces | Gray codes | de Bruijn graph | k-abelian equivalence | COMPUTER SCIENCE, THEORY & METHODS | Jewelry | Lower bounds | Equivalence | Upper bounds | Alphabets | Binary codes | Graphs | Decomposition | Joints | Computer Science | Discrete Mathematics

Journal Article

Discrete Mathematics, ISSN 0012-365X, 04/2015, Volume 338, Issue 4, pp. 655 - 660

We investigate new equivalence relations on the set of Dyck paths relatively to the three statistics of double rises, peaks and valleys. Two Dyck paths are...

Equivalence relation | Motzkin and Fibonacci sequences | Valley | Catalan | Dyck path | Peak | Statistics | Rise | MATHEMATICS | Functions (mathematics) | Equivalence | Mathematical analysis | Valleys | Combinatorics | Mathematics

Equivalence relation | Motzkin and Fibonacci sequences | Valley | Catalan | Dyck path | Peak | Statistics | Rise | MATHEMATICS | Functions (mathematics) | Equivalence | Mathematical analysis | Valleys | Combinatorics | Mathematics

Journal Article

Discrete Mathematics, ISSN 0012-365X, 10/2016, Volume 339, Issue 10, pp. 2557 - 2572

Two paths are equivalent modulo a given string , whenever they have the same length and the positions of the occurrences of are the same in both paths. This...

Ballot path | Dyck path | String | MATHEMATICS | DYCK PATHS | STATISTICS | ENUMERATION | Equivalence | Mathematical analysis | Strings

Ballot path | Dyck path | String | MATHEMATICS | DYCK PATHS | STATISTICS | ENUMERATION | Equivalence | Mathematical analysis | Strings

Journal Article

Journal of Integer Sequences, 2015, Volume 18, Issue 7

Journal Article

Computers and Mathematics with Applications, ISSN 0898-1221, 2009, Volume 57, Issue 10, pp. 1638 - 1644

Let be the characteristic polynomial of a graph . Two graphs and are cospectral, denoted by , if . By we denote the cospectral equivalence class determined by...

Adjacency spectrum | Cospectral graph | Cospectral equivalence class | Spectral radius | DS-graph | PATH | MATHEMATICS, APPLIED | INDEX | SPECTRAL CHARACTERIZATION | ROOT-2+ROOT-5

Adjacency spectrum | Cospectral graph | Cospectral equivalence class | Spectral radius | DS-graph | PATH | MATHEMATICS, APPLIED | INDEX | SPECTRAL CHARACTERIZATION | ROOT-2+ROOT-5

Journal Article

Linear Algebra and Its Applications, ISSN 0024-3795, 2007, Volume 427, Issue 2, pp. 161 - 170

For a given connected (undirected) graph , the minimum rank of is defined to be the smallest possible rank over all hermitian matrices whose th entry is...

Graphs | Minimum rank | 05C50 | Hermitian matrices | 15A18 | hermitian matrices | EIGENVALUE | MATHEMATICS | MATHEMATICS, APPLIED | graphs | minimum rank | MAXIMUM MULTIPLICITY | PATH COVER NUMBER

Graphs | Minimum rank | 05C50 | Hermitian matrices | 15A18 | hermitian matrices | EIGENVALUE | MATHEMATICS | MATHEMATICS, APPLIED | graphs | minimum rank | MAXIMUM MULTIPLICITY | PATH COVER NUMBER

Journal Article

Linear Algebra and Its Applications, ISSN 0024-3795, 02/2016, Volume 491, pp. 123 - 137

In this paper we examine an equivalence relation on the set of formal power series with nonzero constant term. This is done both in terms of functional...

Riordan matrix | Extended Riordan matrix | Equivalence class | Lattice path | Functional equation | MATHEMATICS | MATHEMATICS, APPLIED | NUMBERS | RIORDAN MATRICES | ARRAYS

Riordan matrix | Extended Riordan matrix | Equivalence class | Lattice path | Functional equation | MATHEMATICS | MATHEMATICS, APPLIED | NUMBERS | RIORDAN MATRICES | ARRAYS

Journal Article

EXPERIMENTAL MATHEMATICS, ISSN 1058-6458, 2011, Volume 20, Issue 4, pp. 457 - 466

We study equivalence classes relating to the Kazhdan-Lusztig mu(x, w) coefficients in order to help explain the scarcity of distinct values. Each class is...

MATHEMATICS | LATTICE PATHS | PERMUTATIONS | SCHUBERT VARIETIES | Kazhdan-Lusztig polynomials | mu-coefficient | equivalence classes

MATHEMATICS | LATTICE PATHS | PERMUTATIONS | SCHUBERT VARIETIES | Kazhdan-Lusztig polynomials | mu-coefficient | equivalence classes

Journal Article

Discrete Mathematics, ISSN 0012-365X, 04/2019, Volume 342, Issue 4, pp. 997 - 1005

For any pattern of length at most two, we enumerate equivalence classes of Łukasiewicz paths of length where two paths are equivalent whenever the occurrence...

Equivalence relation | Łukasiewicz path | Motzkin path | Dyck path | Patterns | Lukasiewicz path | STRINGS | MATHEMATICS | VALLEYS | PEAKS | DYCK | EQUIVALENCE CLASSES

Equivalence relation | Łukasiewicz path | Motzkin path | Dyck path | Patterns | Lukasiewicz path | STRINGS | MATHEMATICS | VALLEYS | PEAKS | DYCK | EQUIVALENCE CLASSES

Journal Article

ACM Transactions on Algorithms (TALG), ISSN 1549-6325, 11/2007, Volume 3, Issue 4, pp. 45 - es

We describe a new algorithm to enumerate the k shortest simple (loopless) paths in a directed graph and report on its implementation. Our algorithm is based on...

replacement paths | path equivalence class | Loop-free paths | directed paths | Directed paths | Path equivalence class | Replacement paths | MATHEMATICS, APPLIED | COMPUTER SCIENCE, THEORY & METHODS

replacement paths | path equivalence class | Loop-free paths | directed paths | Directed paths | Path equivalence class | Replacement paths | MATHEMATICS, APPLIED | COMPUTER SCIENCE, THEORY & METHODS

Journal Article

11.
An efficient timer based minimum path D-equivalence CDS construction for wireless adhoc networks

Indian Journal of Science and Technology, ISSN 0974-6846, 2015, Volume 8, pp. 24 - 32

Journal Article

12.
Full Text
Local Learning Approaches for Finding Effects of a Specified Cause and Their Causal Paths

ACM Transactions on Intelligent Systems and Technology (TIST), ISSN 2157-6904, 11/2019, Volume 10, Issue 5, pp. 1 - 15

Causal networks are used to describe and to discover causal relationships among variables and data generating mechanisms. There have been many approaches for...

causes and effects | structural learning | causal networks | Causal paths | COMPUTER SCIENCE, INFORMATION SYSTEMS | EQUIVALENCE CLASSES | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE

causes and effects | structural learning | causal networks | Causal paths | COMPUTER SCIENCE, INFORMATION SYSTEMS | EQUIVALENCE CLASSES | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE

Journal Article

Discrete Mathematics, ISSN 0012-365X, 2010, Volume 310, Issue 24, pp. 3648 - 3652

A graph is said to be determined by its adjacency spectrum (DS for short) if there is no other non-isomorphic graph with the same spectrum. In this paper, we...

Adjacency spectrum | Cospectral equivalence class | Cospectral graphs | DS-graph | PATH | MATHEMATICS | TREES | INDEX | Cospectral equivalence

Adjacency spectrum | Cospectral equivalence class | Cospectral graphs | DS-graph | PATH | MATHEMATICS | TREES | INDEX | Cospectral equivalence

Journal Article

Journal of Mathematical Chemistry, ISSN 0259-9791, 10/2016, Volume 54, Issue 9, pp. 1758 - 1776

Symmetry is one of the most fundamental concepts of all nature. We discuss the general theory of symmetry based on theory of semigroups. This includes and...

Orbit | Semifractal | Hidden regularities | Semigroup | Monoid | Theoretical and Computational Chemistry | Chemistry | Hidden symmetry | Fractal | Physical Chemistry | Endomorphism monoid | Inverse semigroup | Color symmetry | Quasicrystal | Automorphism (symmetry) group | Math. Applications in Chemistry | PATHS | MONOIDS | ENDOMORPHISMS | CHEMISTRY, MULTIDISCIPLINARY | GRAPHS | ORDER | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MODELS | REGULARITY | QUASI-CRYSTALS | EQUIVALENCE CLASSES | Research | Mathematical research | Group theory | Symmetry

Orbit | Semifractal | Hidden regularities | Semigroup | Monoid | Theoretical and Computational Chemistry | Chemistry | Hidden symmetry | Fractal | Physical Chemistry | Endomorphism monoid | Inverse semigroup | Color symmetry | Quasicrystal | Automorphism (symmetry) group | Math. Applications in Chemistry | PATHS | MONOIDS | ENDOMORPHISMS | CHEMISTRY, MULTIDISCIPLINARY | GRAPHS | ORDER | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MODELS | REGULARITY | QUASI-CRYSTALS | EQUIVALENCE CLASSES | Research | Mathematical research | Group theory | Symmetry

Journal Article

Statistical Science, ISSN 0883-4237, 8/2007, Volume 22, Issue 3, pp. 430 - 449

Graphical models provide a framework for exploration of multivariate dependence patterns. The connection between graph and statistical model is made by...

Error rates | Gaussian distributions | Statistical graphs | Directed acyclic graphs | Correlations | P values | Markov models | Covariance matrices | Modeling | Vertices | Acyclic directed graph | Covariance graph | Graphical model | Bidirected graph | Concentration graph | Undirected graph | Multiple testing | DAG | Chain graph | Bayesian network | CHAIN GRAPHS | ASSOCIATIONS | PATH DIAGRAMS | COVARIANCE-SELECTION | STATISTICS & PROBABILITY | NETWORKS | bidirected graph | FALSE DISCOVERY RATE | MARKOV EQUIVALENCE CLASSES | concentration graph | chain graph | graphical model | multiple testing | MULTIDIMENSIONAL CONTINGENCY-TABLES | undirected graph | covariance graph | MULTIVARIATE TIME-SERIES | EXPRESSION | acyclic directed graph

Error rates | Gaussian distributions | Statistical graphs | Directed acyclic graphs | Correlations | P values | Markov models | Covariance matrices | Modeling | Vertices | Acyclic directed graph | Covariance graph | Graphical model | Bidirected graph | Concentration graph | Undirected graph | Multiple testing | DAG | Chain graph | Bayesian network | CHAIN GRAPHS | ASSOCIATIONS | PATH DIAGRAMS | COVARIANCE-SELECTION | STATISTICS & PROBABILITY | NETWORKS | bidirected graph | FALSE DISCOVERY RATE | MARKOV EQUIVALENCE CLASSES | concentration graph | chain graph | graphical model | multiple testing | MULTIDIMENSIONAL CONTINGENCY-TABLES | undirected graph | covariance graph | MULTIVARIATE TIME-SERIES | EXPRESSION | acyclic directed graph

Journal Article

Journal of Nonlinear Optical Physics and Materials, ISSN 0218-8635, 06/2015, Volume 24, Issue 2, pp. 1550021 - 1-1550021-27

In the Schrodinger picture, we find explicit solutions for two models of degenerate parametric oscillators in the case of multi-parameter squeezed input...

Ince equation | interaction picture | Wigner function | Ermakov-type system | degenerate parametric amplifier | differential Galois theory | Kovacic algorithm | Time-dependent Schrödinger equation | PHYSICS, APPLIED | MINIMUM-UNCERTAINTY PACKETS | COHERENT STATES | ELECTROMAGNETIC-FIELD | RADIATION-FIELD | Time-dependent Schrodinger equation | HARMONIC-OSCILLATORS | THERMAL NOISE | OPTICS | PATH-INTEGRAL APPROACH | NONLINEAR OPTICS | QUANTUM-THEORY | EQUIVALENCE CLASSES | Operators | Evolution | Mathematical models | Photons | Transformations | Schroedinger equation | Representations | Statistics

Ince equation | interaction picture | Wigner function | Ermakov-type system | degenerate parametric amplifier | differential Galois theory | Kovacic algorithm | Time-dependent Schrödinger equation | PHYSICS, APPLIED | MINIMUM-UNCERTAINTY PACKETS | COHERENT STATES | ELECTROMAGNETIC-FIELD | RADIATION-FIELD | Time-dependent Schrodinger equation | HARMONIC-OSCILLATORS | THERMAL NOISE | OPTICS | PATH-INTEGRAL APPROACH | NONLINEAR OPTICS | QUANTUM-THEORY | EQUIVALENCE CLASSES | Operators | Evolution | Mathematical models | Photons | Transformations | Schroedinger equation | Representations | Statistics

Journal Article

Chemical Biology & Drug Design, ISSN 1747-0277, 06/2006, Volume 67, Issue 6, pp. 395 - 408

A general methodology is presented for analyzing patterns of activity in compound databases, which is based on the use of structural chemotypes and provides a...

chemotype-enrichment plots | chemotypes | NCI AIDS database | paths of activity | equivalence classes | parent-child relationships | chemotype‐enrichment plots | parent–child relationships | Equivalence classes | Paths of activity | Chemotype-enrichment plots | Parent-child relationships | Chemotypes | BIOCHEMISTRY & MOLECULAR BIOLOGY | REVERSE-TRANSCRIPTASE | SETS | IMMUNODEFICIENCY-VIRUS TYPE-1 | INHIBITORS | SOFTWARE | Models, Molecular | Chemistry Techniques, Analytical - methods | Sensitivity and Specificity | Computational Biology | Databases, Factual | Study and teaching | Analysis | Databases

chemotype-enrichment plots | chemotypes | NCI AIDS database | paths of activity | equivalence classes | parent-child relationships | chemotype‐enrichment plots | parent–child relationships | Equivalence classes | Paths of activity | Chemotype-enrichment plots | Parent-child relationships | Chemotypes | BIOCHEMISTRY & MOLECULAR BIOLOGY | REVERSE-TRANSCRIPTASE | SETS | IMMUNODEFICIENCY-VIRUS TYPE-1 | INHIBITORS | SOFTWARE | Models, Molecular | Chemistry Techniques, Analytical - methods | Sensitivity and Specificity | Computational Biology | Databases, Factual | Study and teaching | Analysis | Databases

Journal Article

SIAM Journal on Discrete Mathematics, ISSN 0895-4801, 1998, Volume 11, Issue 1, pp. 94 - 109

We give efficient algorithms for listing equivalence classes of k-ary strings under reversal and permutation of alphabet symbols. As representative of each...

Combinatorial generation | k-paths | Stirling numbers | K-ary strings | Restricted growth function | GENERATING NECKLACES | COLORS | MATHEMATICS, APPLIED | combinatorial generation | restricted growth function | k-ary strings | BEADS

Combinatorial generation | k-paths | Stirling numbers | K-ary strings | Restricted growth function | GENERATING NECKLACES | COLORS | MATHEMATICS, APPLIED | combinatorial generation | restricted growth function | k-ary strings | BEADS

Journal Article

Fiber and Integrated Optics, ISSN 0146-8030, 01/2003, Volume 22, Issue 5, pp. 289 - 303

This article details the evolution of Ethernet into Gigabit Ethernet and how this LAN-based technology has undergone major transformations over time. From its...

1-gigabit ethernet | Single Mode Fiber (SMF) | Frame Check Sequence (FCS) | Dense Wavelength Division Multiplexing (DWDM) | fiber channel | Shielded Twisted Pair (STP) | Synchronous Optical Networks (SONET) | Add-Drop Multiplexor (ADM) | Time Division Multiplexing (TDM) | Media Independent Interface (MII) | Switched Virtual Circuits (SWC) | Physical Layer (PHY) | Label Switched Router (LSR) | Point-to-Point Protocol (PPP) | Link Capacity Adjustment Scheme (LCAS) | Resilient Packet Rings (RPR) | Virtual Concatenation Group (VCG) | Unshielded Twisted Pair (UTP) | SDH Virtual Container (SDH-VC) | ethernet | Physical Medium Dependents (PMDs) | Carrier Sense Multiple Access with Collision Detection (CSMA/CD) | Optical Cross Connect (OXC) | Inter-Packet Gap (IPG) | Optical Circuit (OC) | Packet Over SONET (POS) | Ethernet Over SONET (EOS) | Local Area Networks (LAN) | Generalized Multi-Protocol Label Switching (GMPLS) | Permanent Virtual Circuits (PVC) | Label Edge Router (LER) | Wide Wave Division Multiplexing (WWDM) | Synchronous Payload Envelope (SPE) | Forward Equivalence Class (FEC) | 10-gigabit ethernet | Gigabit Media Independent Interface (GMII) | Network Interface Card (NIC) | Internet Protocol (IP) | Virtual Concatenation (VC) | token ring | Virtual Private Network (VPN) | Label Switched Path (LSP) | Physical Coding Sublayer (PCS) | Multiple Protocol Label Switching (MPLS) | Media Access Control (MAC) | Quality of Service (QOS) | Reconciliation Sublayer (RS) | Metropolitan Area Networks (MAN) | Physical Medium Attachment (PMA) | Wide Area Networks (WAN) | Synchronous Digital Hierarchy (SDH) | Generic Framing Procedure (GFP) | OPTICS

1-gigabit ethernet | Single Mode Fiber (SMF) | Frame Check Sequence (FCS) | Dense Wavelength Division Multiplexing (DWDM) | fiber channel | Shielded Twisted Pair (STP) | Synchronous Optical Networks (SONET) | Add-Drop Multiplexor (ADM) | Time Division Multiplexing (TDM) | Media Independent Interface (MII) | Switched Virtual Circuits (SWC) | Physical Layer (PHY) | Label Switched Router (LSR) | Point-to-Point Protocol (PPP) | Link Capacity Adjustment Scheme (LCAS) | Resilient Packet Rings (RPR) | Virtual Concatenation Group (VCG) | Unshielded Twisted Pair (UTP) | SDH Virtual Container (SDH-VC) | ethernet | Physical Medium Dependents (PMDs) | Carrier Sense Multiple Access with Collision Detection (CSMA/CD) | Optical Cross Connect (OXC) | Inter-Packet Gap (IPG) | Optical Circuit (OC) | Packet Over SONET (POS) | Ethernet Over SONET (EOS) | Local Area Networks (LAN) | Generalized Multi-Protocol Label Switching (GMPLS) | Permanent Virtual Circuits (PVC) | Label Edge Router (LER) | Wide Wave Division Multiplexing (WWDM) | Synchronous Payload Envelope (SPE) | Forward Equivalence Class (FEC) | 10-gigabit ethernet | Gigabit Media Independent Interface (GMII) | Network Interface Card (NIC) | Internet Protocol (IP) | Virtual Concatenation (VC) | token ring | Virtual Private Network (VPN) | Label Switched Path (LSP) | Physical Coding Sublayer (PCS) | Multiple Protocol Label Switching (MPLS) | Media Access Control (MAC) | Quality of Service (QOS) | Reconciliation Sublayer (RS) | Metropolitan Area Networks (MAN) | Physical Medium Attachment (PMA) | Wide Area Networks (WAN) | Synchronous Digital Hierarchy (SDH) | Generic Framing Procedure (GFP) | OPTICS

Journal Article

Fiber and Integrated Optics, ISSN 0146-8030, 2003, Volume 22, Issue 5, pp. 289 - 303

1-gigabit ethernet | Permanent virtual circuits (PVC) | Synchronous digital hierarchy (SDH) | Synchronous payload envelope (SPE) | Media access control (MAC) | Label switched router (LSR) | Ethernet over SONET (EOS) | Generic framing procedure (GFP) | Add-drop multiplexor (ADM) | Virtual concatenation (VC) | Wide wave division multiplexing (WWDM) | Carrier sense multiple access with collision detection (CSMA/CD) | Label edge router (LER) | Switched virtual circuits (SWC) | Network interface card (NIC) | Virtual private network (VPN) | Gigabit media independent interface (GMII) | Physical coding sublayer (PCS) | Frame check sequence (FCS) | Ethernet | Optical circuit (OC) | SDH virtual container (SDH-VC) | Media independent interface (MII) | Inter-packet gap (IPG) | Physical medium dependents (PMDs) | Virtual concatenation group (VCG) | Local area networks (LAN) | Physical medium attachment (PMA) | Link capacity adjustment scheme (LCAS) | Fiber channel | Optical cross connect (OXC) | Single mode fiber (SMF) | 10-gigabit ethernet | Packet over SONET (POS) | Forward equivalence class (FEC) | Synchronous optical networks (SONET) | Multiple protocol label switching (MPLS) | Physical layer (PHY) | Shielded twisted pair (STP) | Dense wavelength division multiplexing (DWDM) | Internet protocol (IP) | Point-to-point protocol (PPP) | Metropolitan area networks (MAN) | Label switched path (LSP) | Reconciliation sublayer (RS) | Generalized multi-protocol label switching (GMPLS) | Token ring | Quality of service (QOS) | Time division multiplexing (TDM) | Wide area networks (WAN) | Resilient packet rings (RPR) | Unshielded twisted pair (UTP)

Journal Article

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