Sentences with phrase «in dynamical systems»

Subsequent computational studies aptly confirm Kolmogorov's insights and have opened up the enormously fruitful field of «chaos in dynamical systems,» which is currently attracting much attention.

Since you have a fat tail and make the distinction between Dragon Kings and black swans, «Self - organized criticality is therefore a signature of quantumlike chaos in dynamical systems.

In an attempt to understand and feel the mathematical concept of strange attractors in dynamical systems, she jumbles her recent obsession for doughnuts, fortune - tellers, hemorrhoids, and things detected in the world».

We have shown that strict determinism can be invoked only if we assume that all second and other higher order (i.e., non-linear) terms are negligible in a dynamical system.

In principle, an incipient bifurcation in a dynamical system could be anticipated (100), by looking at the spectral properties of time series data (101), in particular, extracting the longest system - immanent timescale (τ) from the response of the system to natural variability (102).

Aires, F., and W.B. Rossow, 2003: Inferring instantaneous, multivariate and nonlinear sensitivities for the analysis of feedback processes in a dynamical system: The Lorenz model case study.

Not exact matches

His analysis of the idea of molecular structure from «first principles» shows that if one starts from a description of the molecule as an isolated, dynamical system consisting of the number of electrons and nuclei implied by the stoichiometric formula that interact via electromagnetic forces, one can not even calculate the most important parameters in chemistry, namely, those that describe the molecular structure.8

This relates to the sensitive dependence of non-linear systems to the initial values of its dynamical parameters (often referred as the «butterfly effect,» a phrase coined by the meteorologist E.N. Lorenz).7 In such a system, even the smallest change (or uncertainty) of initial values of a non-linear or dynamically coupled system, show long - term divergence of its phase - map trajectories, leading to the formation of a basin of so - called «strange attractors.»

However, the introduction of quantum mechanical principles in the early part of this century brought about a dramatic change In our notions of causality, by allowing the concept of non-deterministic evolution of dynamical systems to gain ground in the natural sciencein the early part of this century brought about a dramatic change In our notions of causality, by allowing the concept of non-deterministic evolution of dynamical systems to gain ground in the natural scienceIn our notions of causality, by allowing the concept of non-deterministic evolution of dynamical systems to gain ground in the natural sciencein the natural sciences.

In our discussions of chaos or complexity theory, we have established the underlying non-deterministic (Or stochastic) nature of all dynamical systems with interactive and self - organizing component parts.

The history of science provides many examples of this combination of analogy and innovation in the creation of models which were useful in generating theories.4 The «Bohr model» of the atom, in which «planetary» electrons revolve in orbits around a central nucleus, resembles the solar system in certain of its dynamical properties; but the key assumption of quantum jumps between orbits had no classical parallel at all.

Mirzakhani got the Fields Medal for Mathematics in 2014 for her work on complex geometry and dynamical systems.

According to dynamical systems theory, transport barriers exist in complex flows as objects that can not be crossed by other fluid trajectories.

Future observations and studies into the dynamical lifetimes of non-resonant planet - crossing orbits in the far regions of the outer solar system could help to further test the case for the existence and whereabouts of a ninth planet, Malhotra and her co-authors write.

«Taming chaos: Calculating probability in complex systems: A new method efficiently transforms trajectories from dynamical systems into a finite set of variables.»

«Markov partitioning is transforming a continuous trajectory of a dynamical system stored in variables of high resolution into something discrete that can be stored in a finite set of variables with finite resolution, for instance, an alphabet,» said Nicolás Rubido of the Universidad de la República.

Historically, researchers have divided up data from a dynamical system through Markov partitions — a function that describes a point in space in relation to time, such as a model that describes the swing of a pendulum.

But in an animal study published in Nature in 2012, Shenoy and his colleagues reported finding that much more is going on: Motor cortical neurons work as part of an interconnected circuit — a so - called dynamical system — to create rhythmic patterns of neural activity.

Kuang has also maintained an active mathematics research program on dynamical systems — particularly in the area of functional differential equations.

These scientists and research groups have complementary expertise in numerical analysis, computational science, dynamical systems, statistics, and stochastic processes.

Dynamical systems evolve over time, often in complex ways: they include celestial mechanics (the orbits of bodies in the Solar System); financial markets; the weather; and populations in ecosystems.

In their study, Rasio, Rodriguez and colleagues describe in detail the dynamical interaction processes that could form a merging binary black hole systeIn their study, Rasio, Rodriguez and colleagues describe in detail the dynamical interaction processes that could form a merging binary black hole systein detail the dynamical interaction processes that could form a merging binary black hole system.

The open source software package the researchers have designed, known as Microbial Dynamical Systems INference Engine (MDSINE), uses advanced machine learning technologies to accurately predict how microbial communities in the gut will grow and interact over time.

The first group participates in an intensive 4 - week collaborative learning experience on dynamical systems (broadly understood to include stochastic processes), modeling, and computational methods.

The idea is that small variations in the initial conditions of a dynamical system produce large variations in the long term behavior of the system.

The idea that climate behaves like a dynamical system addresses some of the key shortcomings of the conventional view of climate change — the view that looks at the planet as a whole, in terms of averages.

A dynamical systems approach, by contrast, consider climate as a sum of many different parts, each with its own properties, all of them interdependent in ways that are hard to predict.

Avila won for work in the theory of dynamical systems.

One of the most productive scientists in applying dynamical systems theory to climate is Tim Lenton at the University of East Anglia in England.

He has also applied the theory of dynamical systems to solve a long - standing problem in analysis stemming from quantum mechanics.

Their work focuses on complex dynamical systems whose statistical behaviour can be explained in terms of a superposition of simpler underlying dynamics.

Both our brains and, in a way, conventional computers are dynamical systems: They find answers just based on the question and how the computers are constructed, said Rothganger.

Much of complexity theory is grounded in the manipulation of various kinds of mathematical models of complex dynamical systems.

The belt contains essential information about the planetary formation processes, including both the «cold disk» that harbors the objects that are thought to formed in situ with the whole planetary system, and the «hot / scattered disk» that is the refuge of objects that are dynamically scattered into it during the dynamical evolution of the inner solar system.

Chemistry and climate: Atmospheric composition plays an integral role in the climate system, with feedbacks on both dynamical and radiative processes throughout the atmosphere.

The paper, titled «Dynamical Considerations for Life in Multihabitable Planetary Systems» has been accepted for publication in the Astrophysical Journal.

Results, which were published in the June 1 issue of PLoS Computational Biology, have implications for how evolutionary pressures can improve the function of receptor systems by selectively optimizing a few fundamental dynamical parameters.

In particular, multi-star systems provide a dynamical laboratory that can be used to test and refine various planet formation models.

The role of stellar multiplicity in shaping planetary systems is confirmed by this work, although it does not appear as the only source of dynamical excitation.

Such asymmetry would most likely be the result of dynamical sculpting by one or more unseen planets in the system.

Basing on a mathematical idea about the so - called strange nonchaotic attractor (SNA) in the quasi-periodically forced dynamical systems, the currently available re-analyses data are considered.

To think, remember, imagine, and see — all these amazing capacities of the brain come from billions of neurons with quadrillions of precise connections interacting to form the most remarkable dynamical system in the universe.

In these endeavors, we employ and extend tools and ideas from diverse fields, including statistical mechanics, machine learning, dynamical systems theory, and information theory.

While these internal neural processes are being observed, the researchers learn more about how the neural system operates through a method called perturbation, which is intentionally disrupting the dynamical neural system in precise ways in order to better understand the underlying principles that control its activity.

We aim to determine the level of near - infrared exozodiacal dust emission around a sample of 42 nearby main sequence stars with... ▽ More (Abridged) Dust is expected to be ubiquitous in extrasolar planetary systems owing to the dynamical activity of minor bodies.

Work in ergodic theory and dynamical systems, biomathematics (population ecology, population genetics) and evolutionary game theory.

Abstract: (Abridged) Dust is expected to be ubiquitous in extrasolar planetary systems owing to the dynamical activity of minor bodies.

Some researchers assume that a close system evolves into a wide system over millions of years due to dynamical interactions, but others guess that turbulence in a gas cloud fragments the cloud into smaller ones and stars are formed in each small cloud.

In many cases, he applies dynamical methods to Saturn's rings and other planetary ring systems.

However, dynamical systems can also achieve a state in which the attractors that emerge are not stable, but «strange».