Related papers: Distributed Transformations of Hamiltonian Shapes …
Quantum walks on translation invariant regular graphs spread quadratically faster than their classical counterparts. The same coherence that gives them this quantum speedup inhibits, or even stops their spread in the presence of disorder.…
We discuss four off-shell N=4 D=1 supersymmetry transformations, their associated one-dimensional sigma-models and their mutual relations. They are given by I) the (4,4)_{lin} linear supermultiplet (supersymmetric extension of R^4), II) the…
We study the properties of Hamiltonians defined as the generators of transfer matrices in quasi- one-dimensional waveguides. For single- or multi-mode waveguides obeying flux conservation and time-reversal invariance, the Hamiltonians…
We enhanced the total transmission of light through a disordered waveguide with spatially inhomogeneous scattering and loss by shaping the incident wavefront of a laser beam. Using an on-chip tapered lead, we were able to access all input…
The interaction of neural networks with physical equations offers a wide range of applications. We provide a method which enables a neural network to transform objects subject to given physical constraints. Therefore an U-Net architecture…
A non-unitary transformation leading to a Hatano-Nelson problem is performed on an array of equally-spaced optical waveguides. Such transformation produces a non-reciprocal system of waveguides, as the corresponding Hamiltonian becomes…
We consider a scenario in which leaders are required to recruit teams of followers. Each leader cannot recruit all followers, but interaction is constrained according to a bipartite network. The objective for each leader is to reach a state…
A well-known approach to describe the dynamics of an open quantum system is to compute the master equation evolving the reduced density matrix of the system. This approach plays an important role in describing excitation transfer through…
Due to its decentralised, distributed and scalable nature, swarm robotics has great potential for applications ranging from agriculture to environmental monitoring and logistics. Various swarm control methods and algorithms are currently…
Modern continuous-time generative models typically induce \emph{V-shaped} flows: each sample travels independently along a nearly straight trajectory from the prior to the data. Although effective, this independent movement overlooks the…
This work develops a symmetry-based framework for formation control on cycle graphs using Dihedral point-group constraints. We show that enforcing inter-agent reflection symmetries, together with anchoring a single designated agent to its…
We present an algorithm which explores permutation symmetries to describe the time evolution of agent-based epidemic models. The main idea to improve computation times relies on restricting the stochastic process to one sector of the vector…
Leader election is one of the fundamental and well-studied problems in distributed computing. In this paper, we initiate the study of leader election using mobile agents. Suppose $n$ agents are positioned initially arbitrarily on the nodes…
We describe the deformation cohomology of a symplectic groupoid, and use it to study deformations via Moser path methods, proving a symplectic groupoid version of the Moser Theorem. Our construction uses the deformation cohomologies of Lie…
Two mobile agents, starting from different nodes of a network modeled as a graph, and woken up at possibly different times, have to meet at the same node. This problem is known as rendezvous. We consider deterministic distributed rendezvous…
We explore the structure of the $\lambda$-deformed $\sigma$-model action by setting up a perturbative expansion around the free field point corresponding to the identity group element. We include all field interaction terms up to sixth…
Manifold models provide low-dimensional representations that are useful for processing and analyzing data in a transformation-invariant way. In this paper, we study the problem of learning smooth pattern transformation manifolds from image…
We present some arguments why existing methods for representing agents fall short in applications crucial to artificial life. Using a thought experiment involving a fictitious dynamical systems model of the biosphere we argue that the…
Learning influence pathways of a network of dynamically related processes from observations is of considerable importance in many disciplines. In this article, influence networks of agents which interact dynamically via linear dependencies…
This paper is the first paper of three papers in a series, which intend to provide a systematic treatment for the space-filling curves of self-similar sets. In the present paper, we introduce a notion of \emph{linear graph-directed IFS}…