相关论文: Self-Referential Noise and the Synthesis of Three-…
The counterintuitive emergence of order from noise is a central phenomenon in science, ranging from pattern formation and synchronization to order-by-disorder in frustrated systems. While large-scale spatial self-organization induced by…
The analogue of temporal coherence resonance for spatial degrees of freedom is reported. Specifically, we show that spatiotemporal noise is able to optimally extract an intrinsic spatial scale in nonlinear media close to (but before) a…
We study causal inference in a multi-environment setting, in which the functional relations for producing the variables from their direct causes remain the same across environments, while the distribution of exogenous noises may vary. We…
The phenomenon of Stochastic Resonance (SR) is reported in a completely noise-free situation, with the role of thermal noise being taken by low-dimensional chaos. A one-dimensional, piecewise linear map and a pair of coupled…
Stochastic resonance is a non-linear phenomenon, in which the sensitivity of signal detectors can be enhanced by adding random noise to the detector input. Here, we demonstrate that noise can also improve the information flux in recurrent…
Causal inference uses observations to infer the causal structure of the data generating system. We study a class of functional models that we call Time Series Models with Independent Noise (TiMINo). These models require independent residual…
We study a reaction model that presents stochastic resonance purely due to internal noise. This means that the only source of fluctuations comes from the discrete character of the reactants, and no more noises enter into the system. Our…
What is the origin of macroscopic randomness (uncertainty)? This is one of the most fundamental open questions for human being. In this paper, 10000 samples of reliable (convergent), multiple-scale (from 1.0E-60 to 100) numerical…
We show how a recently introduced statistics [Patil et al, Phys. Rev. Lett. 81 5878 (2001)] provides a direct relationship between dimension and predictability in spatiotemporal chaotic systems. Regions of low dimension are identified as…
Can noise be beneficial to machine-learning prediction of chaotic systems? Utilizing reservoir computers as a paradigm, we find that injecting noise to the training data can induce a stochastic resonance with significant benefits to both…
The emergence of localised radial patterns from a Turing instability has been well studied in two and three dimensional settings and predicted for higher spatial dimensions. We prove the existence of localised $(n+1)$-dimensional radial…
Inferring the causal structure of a set of random variables from a finite sample of the joint distribution is an important problem in science. Recently, methods using additive noise models have been suggested to approach the case of…
A novel kind of self-referential square matrix is introduced. A certain subset of the matrix entries record the frequencies of occurrence of each distinct number appearing within the entire matrix. Such squares are necessarily elusive. Our…
We consider two variables that are related to each other by an invertible function. While it has previously been shown that the dependence structure of the noise can provide hints to determine which of the two variables is the cause, we…
The goal of ordinal embedding is to represent items as points in a low-dimensional Euclidean space given a set of constraints in the form of distance comparisons like "item $i$ is closer to item $j$ than item $k$". Ordinal constraints like…
Starting from a suggestion of Einstein on the construction of the concept of space, we elaborate an intrinsic method to obtain space and time transformations between two inertial spaces of reference, mathematically modeled as affine…
In this paper we examine various requirements on the formalisation choices under which self-reference can be adequately formalised in arithmetic. In particular, we study self-referential numberings, which immediately provide a strong notion…
As circuits continue to miniaturize, noise has become a significant obstacle to performance optimization. Stochastic resonance in logic circuits offers an innovative approach to harness noise constructively; however, current implementations…
Transcript of G.J. Chaitin's 2 March 2000 Carnegie Mellon University School of Computer Science Distinguished Lecture. The notion of randomness is taken from physics and applied to pure mathematics in order to shed light on the…
Process Physics models reality as self-organising relational or semantic information using a self-referentially limited neural network model. This generalises the traditional non-process syntactical modelling of reality by taking account of…