Related papers: Generalised Synchronisations, Embeddings, and Appr…
A new explanation of geometric nature of the reservoir computing phenomenon is presented. Reservoir computing is understood in the literature as the possibility of approximating input/output systems with randomly chosen recurrent neural…
We study synchronization in the XX qubit chain subject to local or multi-local amplitude-damping noise. Analyzing the decoherence-free subspace (DFS) structure of the model, we show that it is completely determined by a simple…
Reservoir Computing (RC) has established itself as an efficient paradigm for temporal processing. However, its scalability remains severely constrained by (i) the necessity of processing temporal data sequentially and (ii) the prohibitive…
We establish general conditions under which there exists uniform in time convergence between a stochastic process and its approximated system. These standardised conditions consist of a local in time estimate between the original and the…
Eventually linearizable objects are novel shared memory programming constructs introduced as an analogy to eventual consistency in message-passing systems. However, their behaviors in shared memory systems are so mysterious that very little…
This paper extends the notion of information processing capacity for non-independent input signals in the context of reservoir computing (RC). The presence of input autocorrelation makes worthwhile the treatment of forecasting and filtering…
In this paper we report for the first time on the necessity of the refinement of the concept of generalized chaotic synchronization. We show that the state vectors of the interacting chaotic systems being in the generalized synchronization…
We study the propagation and distribution of information-carrying signals injected in dynamical systems serving as a reservoir computers. A multivariate correlation analysis in tailored replica tests reveals consistency spectra and…
Randomly evolving systems composed by elements which interact among each other have always been of great interest in several scientific fields. This work deals with the synchronization phenomenon, that could be roughly defined as the…
We show how the Loschmidt echo of a product state after a quench to a conformal invariant critical point and its leading finite time corrections can be predicted by using conformal field theories (CFT). We check such predictions with tensor…
The paper investigates the synchronization of a network of identical linear state-space models under a possibly time-varying and directed interconnection structure. The main result is the construction of a dynamic output feedback coupling…
Deep Echo State Networks (DeepESNs) recently extended the applicability of Reservoir Computing (RC) methods towards the field of deep learning. In this paper we study the impact of constrained reservoir topologies in the architectural…
Continuous-time models are a natural choice for irregular and asynchronous data. A central design choice is how to embed discrete observations into continuous time. Interpolation- and imputation-based embeddings reconstruct a continuous…
A generalisation of Scott's information systems \cite{sco82} is presented that captures exactly all L-domains. The global consistency predicate in Scott's definition is relativised in such a way that there is a consistency predicate for…
It is common for researchers to record long, multiple time series from experiments or calculations. But sometimes there are no good models for the systems or no applicable mathematical theorems that can tell us when there are basic…
Observers for systems with Lie group symmetries are an active area of research that is seeing significant impact in a number of practical domains, including aerospace, robotics, and mechatronics. This paper builds on the theory of the…
We extend a recent synchronization analysis of exact finite-state sources to nonexact sources for which synchronization occurs only asymptotically. Although the proof methods are quite different, the primary results remain the same. We find…
This paper proposes a novel and interpretable recurrent neural-network structure using the echo-state network (ESN) paradigm for time-series prediction. While the traditional ESNs perform well for dynamical systems prediction, it needs a…
Generalized chaotic synchronization regime is observed in the unidirectionally coupled one-dimensional Ginzburg-Landau equations. The mechanism resulting in the generalized synchronization regime arising in the coupled spatially extended…
Hybrid systems with memory refer to dynamical systems exhibiting both hybrid and delay phenomena. While systems of this type are frequently encountered in many physical and engineering systems, particularly in control applications, various…