Related papers: Counting Hamiltonian Paths in Transitive Tournamen…

We show that for every positive integer $k$, any tournament can be partitioned into at most $2^{ck}$ $k$-th powers of paths. This result is tight up to the exponential constant. Moreover, we prove that for every $\varepsilon>0$ and every…

Based on known methods for computing the number of distinct score sequences for $n$-vertex tournaments, we develop algorithms for computing the number of distinct score sequences for self-complementary tournaments, strong tournaments, and…

If $T$ is an $n$-vertex tournament with a given number of $3$-cycles, what can be said about the number of its $4$-cycles? The most interesting range of this problem is where $T$ is assumed to have $c\cdot n^3$ cyclic triples for some $c>0$…

Here, we consider numerical methods for stationary mean-field games (MFG) and investigate two classes of algorithms. The first one is a gradient-flow method based on the variational characterization of certain MFG. The second one uses…

In generic Hamiltonian systems tori of regular motion are dynamically separated from regions of chaotic motion in phase space. Quantum mechanically these phase-space regions are coupled by dynamical tunneling. We introduce a semiclassical…

In this paper, we examine various types of ${\mathcal F}$-hypercyclic (${\mathcal F}$-topologically transitive) and disjoint ${\mathcal F}$-hypercyclic (disjoint ${\mathcal F}$-topologically transitive) properties of binary relations over…

Building on previous work by Cameron et al. in [3], we give a recurrence for computing the number of acyclic orientations of complete $k$-partite graphs, which can be implemented to obtain a dynamic programming algorithm running in time…

A Hamiltonian path (cycle) in a graph is a path (cycle, respectively) which passes through all of its vertices. The problems of deciding the existence of a Hamiltonian cycle (path) in an input graph are well known to be NP-complete, and…

Hamilton's equations of motion are local differential equations and boundary conditions are required to determine the solution uniquely. Depending on the choice of boundary conditions, a Hamiltonian may thereby describe several different…

We detect, by using symplectic topology, invariant measures with large rotation vectors for a class of Hamiltonian flows.

With its systematic exploration of probability distributions, Hamiltonian Monte Carlo is a potent Markov Chain Monte Carlo technique; it is an approach, however, ultimately contingent on the choice of a suitable Hamiltonian function. By…

The fractional Hamiltonian analysis of 1+1 dimensional field theory is investigated and the fractional Ostrogradski's formulation is obtained. The fractional path integral of both simple harmonic oscillator with an acceleration-squares part…

Mean-field games (MFGs) are models for large populations of competing rational agents that seek to optimize a suitable functional. In the case of congestion, this functional takes into account the difficulty of moving in high-density areas.…

A Dynamic Programming based polynomial worst case time and space algorithm is described for computing Hamiltonian Path of a directed graph. Complexity constructive proofs along with a tested C++ implementation are provided as well. The…

A combinatorial simplex algorithm is an instance of the simplex method in which the pivoting depends on combinatorial data only. We show that any algorithm of this kind admits a tropical analogue which can be used to solve mean payoff…

We present the basic formulation of Hamilton dynamics in complex phase space. We extend the Hamilton's function by including the imaginary part and find out the corresponding Hamilton's canonical equation of motion. Example of simple…

We study biased {\em orientation games}, in which the board is the complete graph $K_n$, and Maker and Breaker take turns in directing previously undirected edges of $K_n$. At the end of the game, the obtained graph is a tournament. Maker…

We propose path integral description for quantum mechanical systems on compact graphs consisting of N segments of the same length. Provided the bulk Hamiltonian is segment-independent, scale-invariant boundary conditions given by…

A strategy for finding transition paths connecting two stable basins is presented. The starting point is the Hamilton principle of stationary action; we show how it can be transformed into a minimum principle through the addition of…

This paper presents an alternative approach for the computation of trajectory segments on slow manifolds of saddle type. This approach is based on iterative methods rather than collocation-type methods. Compared to collocation methods, that…