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Memory effects are ubiquitous in small-scale systems. They emerge from interactions between accessible and inaccessible degrees of freedom and give rise to evolution equations that are non-local in time. If the characteristic time scales of…
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…
We study the dynamics of quantum memory assist entropy uncertainty for qutrit system coupled to an environment modeled by random matrices. The results show that the effect of relative coupling strength on entropy uncertainty is opposite in…
Uncertainty quantification is vital for decision-making and risk assessment in machine learning. Mean-variance regression models, which predict both a mean and residual noise for each data point, provide a simple approach to uncertainty…
Noise can induce time order in the dynamics of nonlinear dynamical systems. For example, coherence resonance occurs in various neuron models driven by a noise. In studies of coherence resonance, ensemble-averaged measures of the coherence…
We consider binary infinite order stochastic chains perturbed by a random noise. This means that at each time step, the value assumed by the chain can be randomly and independently flipped with a small fixed probability. We show that the…
We perform network analysis of a system described by the master equation to estimate the lower bound of the steady-state current noise, starting from the level 2.5 large deviation function and using the graph theory approach. When the…
The uncertainty principle sets limit on our ability to predict the values of two incompatible observables measured on a quantum particle simultaneously. This principle can be stated in various forms. In quantum information theory, it is…
Classifying the information content of neural spike trains in a linguistic endeavor, an uncertainty relation emerges between the bit size of a word and its duration. This uncertainty is associated with the task of synchronizing the spike…
We analyse the effect of intrinsic fluctuations on the properties of bistable stochastic systems with time scale separation operating under1 quasi-steady state conditions. We first formulate a stochastic generalisation of the quasi-steady…
The retrieval capabilities of associative neural networks can be impaired by different kinds of noise: the fast noise (which makes neurons more prone to failure), the slow noise (stemming from interference among stored memories), and…
Neurons in the central nervous system are affected by complex and noisy signals due to fluctuations in their cellular environment and in the inputs they receive from many other cells 1,2. Such noise usually increases the probability that a…
We investigate the dynamics of quantum correlations (QC) under the effects of reservoir memory, as a resource for quantum information and computation tasks. Quantum correlations of two-qubit systems are used for implementing quantum…
Reservoir computing is a recent trend in neural networks which uses the dynamical perturbations on the phase space of a system to compute a desired target function. We present how one can formulate an expectation of system performance in a…
Designing robust loss functions is popular in learning with noisy labels while existing designs did not explicitly consider the overfitting property of deep neural networks (DNNs). As a result, applying these losses may still suffer from…
By introducing extrinsic noise as well as intrinsic uncertainty into a network with stochastic events, this paper studies the dynamics of the resulting Markov random network and characterizes a novel phenomenon of intermittent…
The underdamped, non-linear, generalized Langevin equation is widely used to model coarse-grained dynamics of soft and biological materials. By means of a projection operator formalism, we show under which approximations this equation can…
A neural correlate of parametric working memory is a stimulus specific rise in neuron firing rate that persists long after the stimulus is removed. Network models with local excitation and broad inhibition support persistent neural…
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…
Recurrent neural networks are a widely used class of neural architectures. They have, however, two shortcomings. First, it is difficult to understand what exactly they learn. Second, they tend to work poorly on sequences requiring long-term…