Celulární automat a CML systémy

The main aim of this thesis is the study of cellular automata and discrete dynamical systems on a lattice. Both tools, cellular automata as well as dynamical systems on a lattice are introduced and elementary properties described. The relation between cellular automata and dynamical system on lattice is derived. The main goal of the thesis is also the use of the cellular automata as that mathematical tool of evolution visualization of discrete dynamical systems. The theory of cellular automata is applied to the discrete dynamical systems on a lattice Laplacian type and implemented in Java language.Hlavním cílem práce je studium vztahu celulárních automatů a diskrétních dynamických systémů na mřížce. Oba nástroje, jak celulární automat tak dynamický systém na mřížce, jsou zavedeny a jejich základní vlastnosti popsány. Vztah mezi celulárními automaty a dynamickými systémy na mřížce je podrobně popsán. Hlavním cílem práce je dále použití nástroje celulárního automatu jako matematického vizualizačního prostředku evoluce diskrétních dynamických systémů. Teorie celulárních automatů je použita na dynamické systémy na mřížce Lamplaceova typu a implementována v prostředí Java.470 - Katedra aplikované matematikyvelmi dobř

Data based identification and prediction of nonlinear and complex dynamical systems

We thank Dr. R. Yang (formerly at ASU), Dr. R.-Q. Su (formerly at ASU), and Mr. Zhesi Shen for their contributions to a number of original papers on which this Review is partly based. This work was supported by ARO under Grant No. W911NF-14-1-0504. W.-X. Wang was also supported by NSFC under Grants No. 61573064 and No. 61074116, as well as by the Fundamental Research Funds for the Central Universities, Beijing Nova Programme.Peer reviewedPostprin

A scalable and fast artificial neural network syndrome decoder for surface codes

Surface code error correction offers a highly promising pathway to achieve scalable fault-tolerant quantum computing. When operated as stabiliser codes, surface code computations consist of a syndrome decoding step where measured stabiliser operators are used to determine appropriate corrections for errors in physical qubits. Decoding algorithms have undergone substantial development, with recent work incorporating machine learning (ML) techniques. Despite promising initial results, the ML-based syndrome decoders are still limited to small scale demonstrations with low latency and are incapable of handling surface codes with boundary conditions and various shapes needed for lattice surgery and braiding. Here, we report the development of an artificial neural network (ANN) based scalable and fast syndrome decoder capable of decoding surface codes of arbitrary shape and size with data qubits suffering from a variety of noise models including depolarising errors, biased noise, and spatially inhomogeneous noise. Based on rigorous training over 50 million random quantum error instances, our ANN decoder is shown to work with code distances exceeding 1000 (more than 4 million physical qubits), which is the largest ML-based decoder demonstration to-date. The established ANN decoder demonstrates an execution time in principle independent of code distance, implying that its implementation on dedicated hardware could potentially offer surface code decoding times of O($\mu$sec), commensurate with the experimentally realisable qubit coherence times. With the anticipated scale-up of quantum processors within the next decade, their augmentation with a fast and scalable syndrome decoder such as developed in our work is expected to play a decisive role towards experimental implementation of fault-tolerant quantum information processing.Comment: 11 pages, 6 figure

On the use of deep learning for phase recovery

Phase recovery (PR) refers to calculating the phase of the light field from its intensity measurements. As exemplified from quantitative phase imaging and coherent diffraction imaging to adaptive optics, PR is essential for reconstructing the refractive index distribution or topography of an object and correcting the aberration of an imaging system. In recent years, deep learning (DL), often implemented through deep neural networks, has provided unprecedented support for computational imaging, leading to more efficient solutions for various PR problems. In this review, we first briefly introduce conventional methods for PR. Then, we review how DL provides support for PR from the following three stages, namely, pre-processing, in-processing, and post-processing. We also review how DL is used in phase image processing. Finally, we summarize the work in DL for PR and outlook on how to better use DL to improve the reliability and efficiency in PR. Furthermore, we present a live-updating resource (https://github.com/kqwang/phase-recovery) for readers to learn more about PR.Comment: 82 pages, 32 figure

Beyond excitation/inhibition imbalance in multidimensional models of neural circuit changes in brain disorders

A leading theory holds that neurodevelopmental brain disorders arise from imbalances in excitatory and inhibitory (E/I) brain circuitry. However, it is unclear whether this one-dimensional model is rich enough to capture the multiple neural circuit alterations underlying brain disorders. Here, we combined computational simulations with analysis of in vivo two-photon Ca2+ imaging data from somatosensory cortex of Fmr1 knock-out (KO) mice, a model of Fragile-X Syndrome, to test the E/I imbalance theory. We found that: (1) The E/I imbalance model cannot account for joint alterations in the observed neural firing rates and correlations; (2) Neural circuit function is vastly more sensitive to changes in some cellular components over others; (3) The direction of circuit alterations in Fmr1 KO mice changes across development. These findings suggest that the basic E/I imbalance model should be updated to higher dimensional models that can better capture the multidimensional computational functions of neural circuits

Field-control, phase-transitions, and life's emergence

Instances of critical-like characteristics in living systems at each organizational level as well as the spontaneous emergence of computation (Langton), indicate the relevance of self-organized criticality (SOC). But extrapolating complex bio-systems to life's origins, brings up a paradox: how could simple organics--lacking the 'soft matter' response properties of today's bio-molecules--have dissipated energy from primordial reactions in a controlled manner for their 'ordering'? Nevertheless, a causal link of life's macroscopic irreversible dynamics to the microscopic reversible laws of statistical mechanics is indicated via the 'functional-takeover' of a soft magnetic scaffold by organics (c.f. Cairns-Smith's 'crystal-scaffold'). A field-controlled structure offers a mechanism for bootstrapping--bottom-up assembly with top-down control: its super-paramagnetic components obey reversible dynamics, but its dissipation of H-field energy for aggregation breaks time-reversal symmetry. The responsive adjustments of the controlled (host) mineral system to environmental changes would bring about mutual coupling between random organic sets supported by it; here the generation of long-range correlations within organic (guest) networks could include SOC-like mechanisms. And, such cooperative adjustments enable the selection of the functional configuration by altering the inorganic network's capacity to assist a spontaneous process. A non-equilibrium dynamics could now drive the kinetically-oriented system towards a series of phase-transitions with appropriate organic replacements 'taking-over' its functions.Comment: 54 pages, pdf fil

The effect of gap junctional coupling on the spatiotemporal patterns of Ca2+ signals and the harmonization of Ca2+-related cellular responses

The calcium ion (Ca²⁺), a universal signaling molecule, is widely recognized to play a fundamental role in the regulation of various biological processes. Agonist–evoked Ca²⁺ signals often manifest as rhythmic changes in the cytosolic free Ca²⁺ concentration (ccyt) called Ca²⁺ oscillations. Stimuli intensity was found to be proportional to the oscillation frequency and the evoked down-steam cellular response. Stochastic receptor expression in individual cells in a cell population inevitably leads to individually different oscillation frequencies and individually different Ca²⁺-related cellular responses. However, in many organs, the neighboring cells have to overcome their individually different sensitivity and produce a synchronized response. Gap junctions are integral membrane structures that enable the direct cytoplasmic exchange of Ca²⁺ ions and InsP₃ molecules between neighboring cells. By simulations, we were able to demonstrate how the strength of intercellular gap junctional coupling in relation to stimulus intensity can modify the spatiotemporal patterns of Ca²⁺ signals and harmonize the Ca²⁺-related cellular responses via synchronization of oscillation frequency. We demonstrate that the most sensitive cells are the wave initiator cells and that a highly sensitive region plays an important role in the determination of the Ca²⁺ phase wave direction. This sensitive region will then also progressively determine the global behavior of the entire system