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We investigate the problem of scheduling the maintenance of edges in a network, motivated by the goal of minimizing outages in transportation or telecommunication networks. We focus on maintaining connectivity between two nodes over time;…

Effective path planning is a pivotal challenge across various domains, from robotics to logistics and beyond. This research is centred on the development and evaluation of the Dynamic Curvature-Constrained Path Planning Algorithm (DCCPPA)…

Given an autohomeomorphism on an ordered topological space or its subspace, we show that it is sometimes possible to introduce a new topology-compatible order on that space so that the same map is monotonic with respect to the new ordering.…

Sampling-based motion planners have proven to be efficient solutions to a variety of high-dimensional, geometrically complex motion planning problems with applications in several domains. The traditional view of these approaches is that…

This paper proposes a discretionary lane selection algorithm. In particular, highway driving is considered as a targeted scenario, where each lane has a different level of traffic flow. When lane-changing is discretionary, it is advised not…

In the context of two illustrative examples from supersymmetric quantum mechanics we show that the semi-classical analysis of the path integral requires complexification of the configuration space and action, and the inclusion of complex…

A salient feature of topological phases are surface states and many of the widely studied physical properties are directly tied to their existence. Although less explored, a variety of topological phases can however similarly be…

We incorporate prior graph topology information into a Neural Controlled Differential Equation (NCDE) to predict the future states of a dynamical system defined on a graph. The informed NCDE infers the future dynamics at the vertices of…

We want to investigate 'spaces' where paths have a 'weight', or 'cost', expressing length, duration, price, energy, etc. The weight function is not assumed to be invariant up to path-reversion. Thus, 'weighted algebraic topology' can be…

We extend Cellular Automata to time-varying discrete geometries. In other words we formalize, and prove theorems about, the intuitive idea of a discrete manifold which evolves in time, subject to two natural constraints: the evolution does…

Sampled semantics of timed automata is a finite approximation of their dense time behavior. While the former is closer to the actual software or hardware systems with a fixed granularity of time, the abstract character of the latter makes…

The aim of this paper is to show that Digital Signal Processors (DSPs) can be used to efficiently implement complex algorithms. As an example we have chosen the problem of enumerating closed two-dimensional random paths. An Evaluation…

Dynamic memory issues are hard to locate and may cost much of a development project's efforts and was repeatedly reported similarly afterwards independently by different persons. Verification as one formal method may proof a given program's…

Developing multithreaded software is an extremely challenging task, even for experienced programmers. The challenge does not end after the code is written. There are other tasks associated with a development process that become…

Pathways are integral to systems biology. Their classical representation has proven useful but is inconsistent in the meaning assigned to each arrow (or edge) and inadvertently implies the isolation of one pathway from another. Conversely,…

This article describes a numerical procedure designed to tune the parameters of periodically-driven dynamical systems to a state in which they exhibit rich dynamical behavior. This is achieved by maximizing the diversity of subharmonic…

The topology of artificial neural networks has a significant effect on their performance. Characterizing efficient topology is a field of promising research in Artificial Intelligence. However, it is not a trivial task and it is mainly…

Compact representations of objects is a common concept in computer science. Automated planning can be viewed as a case of this concept: a planning instance is a compact implicit representation of a graph and the problem is to find a path (a…

The links between optimal control of dynamical systems and neural networks have proved beneficial both from a theoretical and from a practical point of view. Several researchers have exploited these links to investigate the stability of…

As robots become more common for both able-bodied individuals and those living with a disability, it is increasingly important that lay people be able to drive multi-degree-of-freedom platforms with low-dimensional controllers. One approach…