Related papers: Supervised and unsupervised learning with numerica…
Many diffusion processes in nature and society were found to be anomalous, in the sense of being fundamentally different from conventional Brownian motion. An important example is the migration of biological cells, which exhibits…
Existing approaches to modeling the dynamics of brain tumor growth, specifically glioma, employ biologically inspired models of cell diffusion, using image data to estimate the associated parameters. In this work, we propose an alternative…
Recent generative adversarial networks (GANs) are able to generate impressive photo-realistic images. However, controllable generation with GANs remains a challenging research problem. Achieving controllable generation requires semantically…
The recent advances in cancer immunotherapy boosted the development of tumor-immune system models aiming to provide mechanistic understanding and indicate more efficient treatment regimes. However, the complexity of such models, their…
We propose an iterative algorithm to investigate the cooperative evolution dominated by information encoded within state spaces in a random quantum cellular automaton. Inspired by the 2-gram model in statistical linguistics, the updates of…
Understanding complex quantum dynamics in realistic materials requires insight into the underlying correlations dominating the interactions between the participating particles. Due to the wealth of information involved in these processes,…
Drawing the quantum phase diagram of a many-body system in the parameter space of its Hamiltonian can be seen as a learning problem, which implies labelling the corresponding ground states according to some classification criterium that…
We investigate the ability of a genetic algorithm to design cellular automata that perform computations. The computational strategies of the resulting cellular automata can be understood using a framework in which ``particles'' embedded in…
The ability of a brain or a neural network to efficiently learn depends crucially on both the task structure and the learning rule. Previous works have analyzed the dynamical equations describing learning in the relatively simplified…
Deep convolutional neural networks (CNNs) have demonstrated remarkable success in computer vision by supervisedly learning strong visual feature representations. However, training CNNs relies heavily on the availability of exhaustive…
Given that observational and numerical climate data are being produced at ever more prodigious rates, increasingly sophisticated and automated analysis techniques have become essential. Deep learning is quickly becoming a standard approach…
We present a data-driven learning approach for unknown nonautonomous dynamical systems with time-dependent inputs based on dynamic mode decomposition (DMD). To circumvent the difficulty of approximating the time-dependent Koopman operators…
Quantum cellular automata are alternative quantum-computing paradigms to quantum Turing machines and quantum circuits. Their working mechanisms are inherently automated, therefore measurement free, and they act in a translation invariant…
The day we understand the time evolution of subcellular elements at a level of detail comparable to physical systems governed by Newton's laws of motion seems far away. Even so, quantitative approaches to cellular dynamics add to our…
Learning in the brain is poorly understood and learning rules that respect biological constraints, yet yield deep hierarchical representations, are still unknown. Here, we propose a learning rule that takes inspiration from neuroscience and…
This paper presents EINCASM, a prototype system employing a novel framework for studying emergent intelligence in organisms resembling slime molds. EINCASM evolves neural cellular automata with NEAT to maximize cell growth constrained by…
Stochastic neural networks are a prototypical computational device able to build a probabilistic representation of an ensemble of external stimuli. Building on the relationship between inference and learning, we derive a synaptic plasticity…
Cellular automata (CA) are discrete-time dynamical systems with local update rules on a lattice. Despite their elementary definition, CA support a wide spectrum of macroscopic phenomena central to statistical physics: equilibrium and…
A universal map is derived for all deterministic 1D cellular automata (CA) containing no freely adjustable parameters. The map can be extended to an arbitrary number of dimensions and topologies and its invariances allow to classify all CA…
We study networks representing the dynamics of elementary 1-d cellular automata (CA) on finite lattices. We analyze scaling behaviors of both local and global network properties as a function of system size. The scaling of the largest node…