Related papers: Bounds on the number of time steps for simulating …
The most efficient way to calculate strong bisimilarity is by calculation the relational coarsest partition on a transition system. We provide the first linear time algorithm to calculate strong bisimulation using parallel random access…
Inductive Recommender Systems are capable of recommending for new users and with new items thus avoiding the need to retrain after new data reaches the system. However, these methods are still trained on all the data available, requiring…
We base ourselves on the construction of the two-dimensional random interlacements [12] to define the one-dimensional version of the process. For this constructions we consider simple random walks conditioned on never hitting the origin,…
We propose the use of quantum optical systems to perform universal simulation of quantum dynamics. Two specific implementations that require present technology are put forward for illustrative purposes. The first scheme consists of neutral…
We prove exact bounds on the time complexity of distributed graph colouring. If we are given a directed path that is properly coloured with $n$ colours, by prior work it is known that we can find a proper 3-colouring in $\frac{1}{2}…
We give a series of new lower bounds on the minimum number of vertices required by a graph to contain every graph of a given family as induced subgraph. In particular, we show that this induced-universal graph for $n$-vertex planar graphs…
The cover time of a finite connected graph is the expected number of steps needed for a simple random walk on the graph to visit all vertices of the graph. It is known that the cover time of any finite connected $n$-vertex graph is at least…
Several inequalities are proved for the mixing time of discrete-time quantum walks on finite graphs. The mixing time is defined differently than in Aharonov, Ambainis, Kempe and Vazirani (2001) and it is found that for particular examples…
We perform a systematic comparison of various numerical schemes for the approximation of interface problems. We consider unfitted approaches in view of their application to possibly moving configurations. Particular attention is paid to the…
Consider the random subgraph process on a base graph $G$ with $n$ vertices: we generate a sequence $\{G_t\}_{t=0}^{|E(G)|}$ by taking a uniformly random ordering of the edges of $G$ and then adding these edges one by one to the empty graph…
Real physical systems are only understood, experimentally or theoretically, to a finite resolution so in their analysis there is generally an ignorance of possible short-range phenomena. It is also well-known that the boundary conditions of…
Randomly breaking connections in a graph alters its transport properties, a model used to describe percolation. In the case of quantum walks, dynamic percolation graphs represent a special type of imperfections, where the connections appear…
We spot a hole in the area of succinct data structures for graph classes from a universe of size at most $n^n$. Very often, the input graph is labeled by the user in an arbitrary and easy-to-use way, and the data structure for the graph…
This paper provides a construction method of the nearest graph Laplacian to a matrix identified from measurement data of graph Laplacian dynamics that include biochemical systems, synchronization systems, and multi-agent systems. We…
Brain simulation, as one of the latest advances in artificial intelligence, facilitates better understanding about how information is represented and processed in the brain. The extreme complexity of human brain makes brain simulations only…
Quantum speed limit focuses on the minimum time scale for a fixed mission and hence is important in quantum information where fast dynamics is usually beneficial. Most existing tools for the depiction of quantum speed limit are the…
We present a new algorithm for exactly solving decision making problems represented as influence diagrams. We do not require the usual assumptions of no forgetting and regularity; this allows us to solve problems with simultaneous decisions…
Recently, random walks on dynamic graphs have been studied because of their adaptivity to the time-varying structure of real-world networks. In general, there is a tremendous gap between static and dynamic graph settings for the lazy simple…
We study Hamiltonicity in graphs obtained as the union of a deterministic $n$-vertex graph $H$ with linear degrees and a $d$-dimensional random geometric graph $G^d(n,r)$, for any $d\geq1$. We obtain an asymptotically optimal bound on the…
We calculate an analytical expression for the terrace-width distribution $P(s)$ for an interacting step system with nearest and next nearest neighbor interactions. Our model is derived by mapping the step system onto a statistically…