Related papers: Directed Transit Functions
We have realized real-time steering of the directed transport in a Brownian motor based on cold atoms in optical lattices, and demonstrate drifts along pre-designed paths. The transport is induced by spatiotemporal asymmetries in the…
The definitions and some basic properties of the linear transports along paths in vector bundles and the normal frames for them are recalled. The formalism is specified on line bundles and applied to a geometrical description of the…
We study directed random graphs (random graphs whose edges are directed) as they evolve in discrete time by the addition of nodes and edges. For two distinct evolution strategies, one that forces the graph to a condition of near acyclicity…
We consider paths in weighted and directed temporal networks, introducing tools to compute sets of paths of high probability. We quantify the relative importance of the most probable path between two nodes with respect to the whole set of…
We present a survey on several mass transportation problems, in which a given mass dynamically moves from an initial configuration to a final one. The approach we consider is the one introduced by Benamou and Brenier in [5], where a…
Transport networks are crucial to the functioning of natural and technological systems. Nature features transport networks that are adaptive over a vast range of parameters, thus providing an impressive level of robustness in supply.…
Transport of ions and small molecules across the cell membrane against electrochemical gradients is catalyzed by integral membrane proteins that use a source of free energy to drive the energetically uphill flux of the transported…
Constructions of directed configuration graphs based on a given bi-degree distribution were introduced in random graph theory some years ago. These constructions lead to graphs where the degrees of two nodes belonging to the same edge are…
We give certain properties which are satisfied by the descendant set of a vertex in an infinite, primitive, distance transitive digraph of finite out-valency and provide a strong structure theory for digraphs satisfying these properties. In…
There is a well-known bijection between parking functions of a fixed length and maximal chains of the noncrossing partition lattice which we can use to associate to each set of parking functions a poset whose Hasse diagram is the union of…
Comparability graphs are graphs which have transitive orientations. The dimension of a poset is the least number of linear orders whose intersection gives this poset. The dimension ${\rm dim}(X)$ of a comparability graph $X$ is the…
A transfunction is a function which maps between sets of finite measures on measurable spaces. In this paper we characterize transfunctions that correspond to Markov operators and to plans; such a transfunction will contain the…
We present a method to extract temporal hypergraphs from sequences of 2-dimensional functions obtained as solutions to Optimal Transport problems. We investigate optimality principles exhibited by these solutions from the point of view of…
A transfunction is a function which maps between sets of finite measures on measurable spaces. Push-forward operators form one important class of examples of transfunctions and are identified with their respective measurable functions. In…
Directed graphs have been widely used in Community Question Answering services (CQAs) to model asymmetric relationships among different types of nodes in CQA graphs, e.g., question, answer, user. Asymmetric transitivity is an essential…
A new approach to find all the transitive orientations for a comparability graph (finite or infinite) is presented. This approach is based on the link between the notion of ``strong'' partitive set and the forcing theory (notions of…
Public transport routes sharing the same grid of streets and tracks are often found to proceed in parallel along shorter or longer sequences of stations. Similar phenomena are observed in other networks built with space consuming links such…
The (parallel linear) transports in tensor spaces generated by derivations of the tensor algebra along paths are axiomatically described. Certain their properties are investigated. Transports along paths defined by derivations of the tensor…
This is an introduction to the M\"obius function of a poset. The chief novelty is in the exposition. We show how order-preserving maps from one poset to another can be used to relate their M\"obius functions. We derive the basic results on…
This article gives an introduction to optimal transport, a mathematical theory that makes it possible to measure distances between functions (or distances between more general objects), to interpolate between objects or to enforce…