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Physical Review Letters, ISSN 0031-9007, 11/2009, Volume 103, Issue 22, p. 225503
Optimal paths play a fundamental role in numerous physical applications ranging from random polymers to brittle fracture, from the flow through porous media to... 
INVASION PERCOLATION | PHYSICS, MULTIDISCIPLINARY | DOMAIN-WALLS | MEDIA | DIRECTED POLYMER PROBLEM | RANDOM NETWORKS | STRONG DISORDER | Physics - Disordered Systems and Neural Networks
Journal Article
Macromolecular Rapid Communications, ISSN 1022-1336, 10/2012, Volume 33, Issue 20, pp. 1731 - 1746
Journal Article
Random Structures & Algorithms, ISSN 1042-9832, 01/2019, Volume 54, Issue 1, pp. 69 - 81
We prove that, with high probability, any 2‐edge‐coloring of a random tournament on n vertices contains a monochromatic path of length Ω(n/log⁡n). This... 
monochromatic oriented path | Ramsey theory | monochromatic directed path | size Ramsey number | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS | MATHEMATICS, APPLIED | Graph theory | Graph coloring | Tournaments & championships | Apexes | Upper bounds | Mathematics - Combinatorics
Journal Article
Information Processing Letters, ISSN 0020-0190, 12/2018, Volume 140, pp. 8 - 12
Given a digraph , two vertices and a non-negative integer , the problem asks whether has a path of length at least from to . We present a simple algorithm that... 
Long directed ([formula omitted])-path | Parameterized algorithm | Long directed cycle | Long directed (s,t)-path | PATHS | COMPUTER SCIENCE, INFORMATION SYSTEMS | Long directed (s, t)-path | Algorithms
Journal Article
Journal of Combinatorial Theory, Series B, ISSN 0095-8956, 03/2019, Volume 135, pp. 238 - 255
Given pairs of vertices of a digraph , how can we test whether there exist vertex-disjoint directed paths from to for ? This is NP-complete in general... 
Disjoint paths | Algorithm | Tournament | Directed graph | MATHEMATICS
Journal Article
Ecology, ISSN 0012-9658, 2/2009, Volume 90, Issue 2, pp. 363 - 368
Journal Article
SIAM JOURNAL ON DISCRETE MATHEMATICS, ISSN 0895-4801, 2018, Volume 32, Issue 2, pp. 1246 - 1260
A key feature of Simonovits' proof of the classic Erdos-Posa theorem is a simple subgraph of the host graph, a frame, that determines the outcome of the... 
PACKING DIRECTED CIRCUITS | MATHEMATICS, APPLIED | INDEPENDENT CIRCUITS | A-paths | THEOREM | PRESCRIBED VERTICES | Erdos-Posa property | PROOF | frame | LONG CYCLES | GRAPHS
Journal Article
SIAM Journal on Discrete Mathematics, ISSN 0895-4801, 2015, Volume 29, Issue 1, pp. 500 - 513
We examine the evolution of the best choice algorithm and the probability of its success from a directed path to the linear order of the same cardinality... 
Secretary problem | Graph power | Directed graph | Best choice | graph power | MATHEMATICS, APPLIED | best choice | directed graph | secretary problem | ALGORITHM | Permutations | Algorithms | Mathematical analysis | Graphs | Evolution | Graph theory | Online | Selectors | Optimization
Journal Article
Discrete Applied Mathematics, ISSN 0166-218X, 10/2019
Journal Article
Ecology, ISSN 0012-9658, 03/2013, Volume 94, Issue 3, pp. 560 - 564
Journal Article
Electronic Notes in Discrete Mathematics, ISSN 1571-0653, 08/2017, Volume 61, pp. 177 - 183
We prove that, with high probability, any 2-edge colouring of a random tournament on vertices contains a monochromatic path of length . This resolves a... 
edge colouring | Random tournament | Size Ramsey number | directed paths
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
Journal Article
Graphs and Combinatorics, ISSN 0911-0119, 11/2018, Volume 34, Issue 6, pp. 1197 - 1202
We present an exact formula for enumerating the simple paths between any two vertices of a graph. Our formula involves the adjacency matrices of the connected... 
Dominating sets | Hamiltonian paths | Self-avoiding walks | Simple cycles | Directed graph | Inclusion–exclusion | MATHEMATICS | CYCLES | COUNT PATHS | Inclusion-exclusion | Apexes | Graph theory | Mathematics - Combinatorics
Journal Article
Handbook of Statistics, ISSN 0169-7161, 2019
We modify Suppes’ probabilistic causality theory by replacing inequalities among probabilities of events by unequal residuals of flipped kernel regression... 
Stochastic dominance | Directed acyclic graphs | Bootstrap inference | Kernel regression | Instrumental variables
Journal Article
Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, ISSN 1539-3755, 10/2013, Volume 88, Issue 4, p. 042118
Following our numerical work [Phys. Rev. Lett. 109, 170602 (2012)] focused upon the 2 + 1 Kardar-Parisi-Zhang (KPZ) equation with flat initial condition, we... 
RANDOM-MEDIA | DISTRIBUTIONS | KPZ EQUATION | PHYSICS, FLUIDS & PLASMAS | UPPER CRITICAL DIMENSION | GROWTH-PROCESSES | FLUCTUATIONS | INTERFACES | DIRECTED POLYMERS | PHYSICS, MATHEMATICAL | SCALING FUNCTIONS | RANDOM MATRICES
Journal Article
IEEE Transactions on Energy Conversion, ISSN 0885-8969, 7/2019, Volume 34, Issue 4, pp. 1 - 1
During the design process of the asymmetric-paths winding, the optimization between the asymmetric degree and the tidiness of end connections is still a... 
Coils | Windings | Wires | Stator windings | winding design | directed graph | Conductors | connection optimization | ac machines | Asymmetric-paths winding | Indexes | Optimization
Journal Article
Discrete Mathematics, ISSN 0012-365X, 03/2016, Volume 339, Issue 3, pp. 1116 - 1139
This paper is devoted to the study of non-simple directed lattice paths running between two fixed points and for which the set of allowed steps contains... 
Simple directed lattice paths | Bijective combinatorics | MATHEMATICS | TREES | NUMBERS | MOTZKIN PATHS | ENUMERATION
Journal Article
Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8121, 12/2010, Volume 43, Issue 48, p. 485006
The adsorption of a Motzkin path with lifted endpoints onto an adsorbing line is examined as a model of polymer adsorption. The partition function of this... 
TRANSITION | DESORPTION | FORCE | PHYSICS, MULTIDISCIPLINARY | MOLECULE | CHAINS | DIRECTED-WALK MODEL | ADSORPTION | PHYSICS, MATHEMATICAL | POLYMER SUBJECT
Journal Article
Genes and Development, ISSN 0890-9369, 01/2008, Volume 22, Issue 1, pp. 1 - 7