Related papers: Circuit Walks in Integral Polyhedra
In a temporal graph, each edge is available at specific points in time. Such an availability point is often represented by a ''temporal edge'' that can be traversed from its tail only at a specific departure time, for arriving in its head…
Chordal clutters in the sense of [14] and [3] are defined via simplicial orders. Their circuit ideal has a linear resolution, independent of the characteristic of the base field. We show that any Betti sequence of an ideal with linear…
This article focuses on integrating path-planning and control with specializing on the unique needs of robotic unicycles. A unicycle design is presented which is capable of accelerating/breaking and carrying out a variety of maneuvers. The…
There are presently two models for quantum walks on graphs. The "coined" walk uses discrete time steps, and contains, besides the particle making the walk, a second quantum system, the coin, that determines the direction in which the…
Graph vertex embeddings based on random walks have become increasingly influential in recent years, showing good performance in several tasks as they efficiently transform a graph into a more computationally digestible format while…
Incorporating higher-order interactions in information processing enables us to build more accurate models, gain deeper insights into complex systems, and address real-world challenges more effectively. However, existing methods, such as…
We define and investigate the properties of the jaggedness of path integral trajectories. The new quantity is shown to be scale invariant and to satisfy a self-averaging property. Jaggedness allows for a classification of path integral…
To design efficient parallel algorithms, some recent papers showed that many sequential iterative algorithms can be directly parallelized but there are still challenges in achieving work-efficiency and high-parallelism. Work-efficiency can…
The monography presents a new algorithm for finding the clique of maximal length in a nonseparable graph. The algorithm is based on the properties of the representation of a clique as a subset of the set of cycles with a length of three,…
Photonic circuits, engineered to couple optical modes according to a specific map, serve as processors for classical and quantum light. The number of components typically scales with that of processed modes, thus correlating system size,…
Irregular pyramids are made of a stack of successively reduced graphs embedded in the plane. Such pyramids are used within the segmentation framework to encode a hierarchy of partitions. The different graph models used within the irregular…
The hamiltonian circuit polytope is the convex hull of feasible solutions for the circuit constraint, which provides a succinct formulation of the traveling salesman and other sequencing problems. We study the polytope by establishing its…
Threads as considered in basic thread algebra are primarily looked upon as behaviours exhibited by sequential programs on execution. It is a fact of life that sequential programs are often fragmented. Consequently, fragmented program…
This paper focuses on vertices of the master corner polyhedra $P(G,g_0),$ the core of the group-theoretical approach to integer linear programming. We introduce two combinatorial operations that transform each vertex of $P(G,g_0)$ to…
Random walks are the simplest way to explore or search a graph, and have revealed a very useful tool to investigate and characterize the structural properties of complex networks from the real world, e.g. they have been used to identify the…
We present an efficient general method for realizing a quantum walk operator corresponding to an arbitrary sparse classical random walk. Our approach is based on Grover and Rudolph's method for preparing coherent versions of efficiently…
Regular incidence complexes are combinatorial incidence structures generalizing regular convex polytopes, regular complex polytopes, various types of incidence geometries, and many other highly symmetric objects. The special case of…
Trajectories in logarithmic potentials are investigated by taking as example the motion of an electron within a cylindrical capacitor. The solution of the equation of motion in plane polar coordinates, (r,{\phi}) is attained by forming a…
Polymorphic circuits are a special kind of circuits which possess multiple build-in functions, and these functions are activated by environment parameters, like temperature, light and VDD. The behavior of a polymorphic circuit can be…
We show that, for planar point sets, the number of non-crossing Hamiltonian paths is polynomially bounded in the number of non-crossing paths, and the number of non-crossing Hamiltonian cycles (polygonalizations) is polynomially bounded in…