Related papers: On the cost of simulating a parallel Boolean autom…
A multi-cell cluster-free NOMA framework is proposed, where both intra-cell and inter-cell interference are jointly mitigated via flexible cluster-free successive interference cancellation (SIC) and coordinated beamforming design. The joint…
We investigate the scheduling of $n$ jobs divided into $c$ classes on $m$ identical parallel machines. For every class there is a setup time which is required whenever a machine switches from the processing of one class to another class.…
In the paper we consider the problem of scheduling $n$ identical jobs on 3 uniform machines with speeds $s_1, s_2,$ and $s_3$ to minimize the schedule length. We assume that jobs are subjected to some kind of mutual exclusion constraints,…
We investigate the trade-off between the robustness against random and targeted removal of nodes from a network. To this end we utilize the stochastic block model to study ensembles of infinitely large networks with arbitrary large-scale…
We study the adjacency graph of bubbles---i.e., complementary connected components---of an SLE$_{\kappa}$ curve for $\kappa \in (4,8)$, with two such bubbles considered to be adjacent if their boundaries intersect. We show that this…
It is an increasingly important problem to study conditions on the structure of a network that guarantee a given behavior for its underlying dynamical system. In this paper we report that a Boolean network may fall within the chaotic…
We consider a class of random loop models (including the random interchange process) that are parametrised by a time parameter $\beta\geq 0$. Intuitively, larger $\beta$ means more randomness. In particular, at $\beta=0$ we start with loops…
We consider the following question on the relationship between the asymptotic behaviours of asynchronous dynamics of Boolean networks and their regulatory structures: does the presence of a cyclic attractor imply the existence of a local…
We study the problem of example-based procedural texture synthesis using highly compact models. Given a sample image, we use differentiable programming to train a generative process, parameterised by a recurrent Neural Cellular Automata…
This paper considers the conditional fault tolerance, $h$-super connectivity $\kappa^{h}$ and $h$-super edge-connectivity $\lambda^{h}$ of the hierarchical cubic network $HCN_n$, an attractive alternative network to the hypercube, and shows…
We study optimal distributed first-order optimization algorithms when the network (i.e., communication constraints between the agents) changes with time. This problem is motivated by scenarios where agents experience network malfunctions.…
A path in an edge-colored graph is called proper if no two consecutive edges of the path receive the same color. For a connected graph $G$, the proper connection number $pc(G)$ of $G$ is defined as the minimum number of colors needed to…
Known simulations of random access machines (RAMs) or parallel RAMs (PRAMs) by Boolean circuits incur significant polynomial blowup, due to the need to repeatedly simulate accesses to a large main memory. Consider a single modification to…
A graph in a certain graph class is called minimizing if the least eigenvalue of the adjacency matrix of the graph attains the minimum among all graphs in that class. Bell {\it et al.} have characterized the minimizing graphs in the class…
We study adaptive network coding (NC) for scheduling real-time traffic over a single-hop wireless network. To meet the hard deadlines of real-time traffic, it is critical to strike a balance between maximizing the throughput and minimizing…
Scenario-based stochastic optimal control problems suffer from the curse of dimensionality as they can easily grow to six and seven figure sizes. First-order methods are suitable as they can deal with such large-scale problems, but may fail…
Reconfiguration schedules, i.e., sequences that gradually transform one solution of a problem to another while always maintaining feasibility, have been extensively studied. Most research has dealt with the decision problem of whether a…
A Boolean network (BN) is a discrete dynamical system defined by a Boolean function that maps to the domain itself. A trap space of a BN is a generalization of a fixed point, which is defined as the sub-hypercubes closed by the function of…
We present a novel parallelisation scheme that simplifies the adaptation of learning algorithms to growing amounts of data as well as growing needs for accurate and confident predictions in critical applications. In contrast to other…
The local minimum degree of a graph is the minimum degree reached by means of a series of local complementations. In this paper, we investigate on this quantity which plays an important role in quantum computation and quantum error…