Adaptive, locally linear models of complex dynamics Costa, Antonio C.; Ahamed, Tosif; Stephens, Greg J.
Proceedings of the National Academy of Sciences - PNAS,
01/2019, Letnik:
116, Številka:
5
Journal Article
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The dynamics of complex systems generally include high-dimensional, nonstationary, and nonlinear behavior, all of which pose fundamental challenges to quantitative understanding. To address these ...difficulties, we detail an approach based on local linear models within windows determined adaptively from data. While the dynamics within each window are simple, consisting of exponential decay, growth, and oscillations, the collection of local parameters across all windows provides a principled characterization of the full time series. To explore the resulting model space, we develop a likelihood-based hierarchical clustering, and we examine the eigenvalues of the linear dynamics. We demonstrate our analysis with the Lorenz system undergoing stable spiral dynamics and in the standard chaotic regime. Applied to the posture dynamics of the nematode Caenorhabditis elegans, our approach identifies fine-grained behavioral states and model dynamics which fluctuate about an instability boundary, and we detail a bifurcation in a transition from forward to backward crawling. We analyze whole-brain imaging in C. elegans and show that global brain dynamics is damped away from the instability boundary by a decrease in oxygen concentration. We provide additional evidence for such near-critical dynamics from the analysis of electrocorticography in monkey and the imaging of a neural population from mouse visual cortex at single-cell resolution.
What aspects of neuronal activity distinguish the conscious from the unconscious brain? This has been a subject of intense interest and debate since the early days of neurophysiology. However, as any ...practicing anesthesiologist can attest, it is currently not possible to reliably distinguish a conscious state from an unconscious one on the basis of brain activity. Here we approach this problem from the perspective of dynamical systems theory. We argue that the brain, as a dynamical system, is self-regulated at the boundary between stable and unstable regimes, allowing it in particular to maintain high susceptibility to stimuli. To test this hypothesis, we performed stability analysis of high-density electrocorticography recordings covering an entire cerebral hemisphere in monkeys during reversible loss of consciousness. We show that, during loss of consciousness, the number of eigenmodes at the edge of instability decreases smoothly, independently of the type of anesthetic and specific features of brain activity. The eigenmodes drift back toward the unstable line during recovery of consciousness. Furthermore, we show that stability is an emergent phenomenon dependent on the correlations among activity in different cortical regions rather than signals taken in isolation. These findings support the conclusion that dynamics at the edge of instability are essential for maintaining consciousness and provide a novel and principled measure that distinguishes between the conscious and the unconscious brain.
What distinguishes brain activity during consciousness from that observed during unconsciousness? Answering this question has proven difficult because neither consciousness nor lack thereof have universal signatures in terms of most specific features of brain activity. For instance, different anesthetics induce different patterns of brain activity. We demonstrate that loss of consciousness is universally and reliably associated with stabilization of cortical dynamics regardless of the specific activity characteristics. To give an analogy, our analysis suggests that loss of consciousness is akin to depressing the damper pedal on the piano, which makes the sounds dissipate quicker regardless of the specific melody being played. This approach may prove useful in detecting consciousness on the basis of brain activity under anesthesia and other settings.
Systems poised at a dynamical critical regime, between order and disorder, have been shown capable of exhibiting complex dynamics that balance robustness to external perturbations and rich ...repertoires of responses to inputs. This property has been exploited in artificial network classifiers, and preliminary results have also been attained in the context of robots controlled by Boolean networks. In this work, we investigate the role of dynamical criticality in robots undergoing online adaptation, i.e., robots that adapt some of their internal parameters to improve a performance metric over time during their activity. We study the behavior of robots controlled by random Boolean networks, which are either adapted in their coupling with robot sensors and actuators or in their structure or both. We observe that robots controlled by critical random Boolean networks have higher average and maximum performance than that of robots controlled by ordered and disordered nets. Notably, in general, adaptation by change of couplings produces robots with slightly higher performance than those adapted by changing their structure. Moreover, we observe that when adapted in their structure, ordered networks tend to move to the critical dynamical regime. These results provide further support to the conjecture that critical regimes favor adaptation and indicate the advantage of calibrating robot control systems at dynamical critical states.
In theoretical biology,
refers to the ability of a biological system to function properly even under perturbation of basic parameters (e.g., temperature or pH), which in mathematical models is ...reflected in not needing to fine-tune basic parameter constants;
refers to the ability of a system to switch functions or behaviors easily and effortlessly. While there are extensive explorations of the concept of robustness and what it requires mathematically, understanding flexibility has proven more elusive, as well as also elucidating the apparent opposition between what is required mathematically for models to implement either. In this paper we address a number of arguments in theoretical neuroscience showing that both robustness and flexibility can be attained by systems that poise themselves at the onset of a large number of dynamical bifurcations, or
, and how such poising can have a profound influence on integration of information processing and function. Finally, we examine critical map lattices, which are coupled map lattices where the coupling is dynamically critical in the sense of having purely imaginary eigenvalues. We show that these map lattices provide an explicit connection between dynamical criticality in the sense we have used and "edge of chaos" criticality.
Systems of dense spheres interacting through very short-ranged attraction are known from theory, simulations and colloidal experiments to exhibit dynamical
reentrance
. Their liquid state can thus be ...fluidized at higher densities than possible in systems with pure repulsion or with long-ranged attraction. A recent mean-field, infinite-dimensional calculation predicts that the dynamical arrest of the fluid can be further delayed by adding a longer-ranged repulsive contribution to the short-ranged attraction. We examine this proposal by performing extensive numerical simulations in a three-dimensional system. We first find the short-ranged attraction parameters necessary to achieve the densest liquid state, and then explore the parameter space for an additional longer-ranged repulsion that could further enhance reentrance. In the family of systems studied, no significant (within numerical accuracy) delay of the dynamical arrest is observed beyond what is already achieved by the short-ranged attraction. Possible explanations are discussed.
Mounting experimental and theoretical results indicate that neural systems are poised near a critical state. In human subjects, however, most evidence comes from functional MRI studies, an indirect ...measurement of neuronal activity with poor temporal resolution. Electrocorticography (ECoG) provides a unique window into human brain activity: each electrode records, with high temporal resolution, the activity resulting from the sum of the local field potentials of ∼10(5) neurons. We show that the human brain ECoG recordings display features of self-regulated dynamical criticality: dynamical modes of activation drift around the critical stability threshold, moving in and out of the unstable region and equilibrating the global dynamical state at a very fast time scale. Moreover, the analysis also reveals differences between the resting state and a motor task, associated with increased stability of a fraction of the dynamical modes.
Mesoscopic ferroic glasses such as martensitic strain glass Ti
50−
x
Ni
50+
x
, magnetic cluster glass La
0.7
Ca
0.3
Mn
0.7
Cd
0.3
O
3
, and superdipolar relaxor PbMg
1/3
Nb
2/3
O
3
(PMN) undergo ...glass transitions preceded by mesoscopic precursor patterns - elastic or magnetic tweed or polar nanoregions (PNR), respectively. In PMN the PNR glass transition at T
g
≈ 240 K reveals glassy dynamic criticality and non-ergodicity of the field-induced low-T phase similar to that of a superspin glass of fixed magnetic nanoparticles in a diamagnetic environment. A final ferroelectric domain state is reached at T
p
≈ 213 K via PNR percolation, which is absent in weak relaxors like BaTi
0.65
Zr
0.35
O
3
(BTZ35).
Random electric fields (RF) due to charge disorder are at the origin of polar nanoregions (PNR) in the cubic relaxor PbMg
1/3
Nb
2/3
O
3
. They initiate Lacroix-Béné-type Cole-Cole semicircles, which ...achieve Cole-Davidson skew and dynamic power law criticality upon approaching superdipolar glass freezing. Below T
g
≈ 240 K percolation of PNR into microdomains is evidenced by interfacial creep and relaxation via Cole-Cole diagrams. Similar behavior occurs in uniaxial Sr
0.8
Ba
0.2
Nb
2
O
6
(T
g
≈ 301 K). In contrast, matrix isolated ferromagnetic nanoparticles in CoFe/Al
2
O
3
multilayers without RF interaction lack all of these effects except superglassy critical dynamics at T
g
≈ 46 K.
Quenched random fields (RFs) are well-known to be a basic driving force of the peculiar behavior of relaxor ferroelectrics such as PbMg
1/3
Nb
2/3
O
3
(PMN), Sr
x
Ba
1-x
Nb
2
O
6
(SBN), and BaTi
1-x
...Zr
x
O
3
(BTZ), hence, giving rise to strong frequency dispersion of the dielectric response, an apparent lack of macroscopic symmetry breaking at low temperatures, and the formation of polar nanoregions (PNRs) thus creating random 'domain states'. A fundamental completion of relaxor physics toward a superdipolar cluster glass ground state of the randomly interacting PNRs appears necessary as evidenced by dynamic criticality and non-ergodic aging and rejuvenation processes.
An asset’s risk is a useful indicator for determining optimal time of repair/replacement for assets in order to yield minimal operational cost of maintenance. For a successful asset management ...practice, asset-intensive organisations must understand the risk profile associated with their asset portfolio and how this will change over time. Unfortunately, in many risk-based asset management approaches, the only thing that is known to change in the risk profile of the asset is the likelihood (or probability) of failure. The criticality (or consequences of failure) of asset is assumed to be fixed and has considered as more or less a static quantity that is not updated with sufficient frequency as the operating environment changes. This paper proposes a dynamic criticality-based maintenance approach where asset criticality is modeled as a dynamic quantity and changes in asset’s criticality is used to optimize maintenance plans (e.g. determining the optimal repair time/replacement age for an asset over it life cycle period) to have a better risk management and cost savings. An illustrative example is used to demonstrate the effect of implementing dynamic criticality in determining the optimal time of repair for a bridge infrastructure. It is shown that capturing changes in the criticality of the bridge over time and using this understanding in the risk analysis of the bridge provided the opportunity for better maintenance planning resulting to reduction of the total risk.
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