726 research outputs found
Reductions of Hidden Information Sources
In all but special circumstances, measurements of time-dependent processes
reflect internal structures and correlations only indirectly. Building
predictive models of such hidden information sources requires discovering, in
some way, the internal states and mechanisms. Unfortunately, there are often
many possible models that are observationally equivalent. Here we show that the
situation is not as arbitrary as one would think. We show that generators of
hidden stochastic processes can be reduced to a minimal form and compare this
reduced representation to that provided by computational mechanics--the
epsilon-machine. On the way to developing deeper, measure-theoretic foundations
for the latter, we introduce a new two-step reduction process. The first step
(internal-event reduction) produces the smallest observationally equivalent
sigma-algebra and the second (internal-state reduction) removes sigma-algebra
components that are redundant for optimal prediction. For several classes of
stochastic dynamical systems these reductions produce representations that are
equivalent to epsilon-machines.Comment: 12 pages, 4 figures; 30 citations; Updates at
http://www.santafe.edu/~cm
Global Seismic Nowcasting With Shannon Information Entropy.
Seismic nowcasting uses counts of small earthquakes as proxy data to estimate the current dynamical state of an earthquake fault system. The result is an earthquake potential score that characterizes the current state of progress of a defined geographic region through its nominal earthquake "cycle." The count of small earthquakes since the last large earthquake is the natural time that has elapsed since the last large earthquake (Varotsos et al., 2006, https://doi.org/10.1103/PhysRevE.74.021123). In addition to natural time, earthquake sequences can also be analyzed using Shannon information entropy ("information"), an idea that was pioneered by Shannon (1948, https://doi.org/10.1002/j.1538-7305.1948.tb01338.x). As a first step to add seismic information entropy into the nowcasting method, we incorporate magnitude information into the natural time counts by using event self-information. We find in this first application of seismic information entropy that the earthquake potential score values are similar to the values using only natural time. However, other characteristics of earthquake sequences, including the interevent time intervals, or the departure of higher magnitude events from the magnitude-frequency scaling line, may contain additional information
The Computational Complexity of Symbolic Dynamics at the Onset of Chaos
In a variety of studies of dynamical systems, the edge of order and chaos has
been singled out as a region of complexity. It was suggested by Wolfram, on the
basis of qualitative behaviour of cellular automata, that the computational
basis for modelling this region is the Universal Turing Machine. In this paper,
following a suggestion of Crutchfield, we try to show that the Turing machine
model may often be too powerful as a computational model to describe the
boundary of order and chaos. In particular we study the region of the first
accumulation of period doubling in unimodal and bimodal maps of the interval,
from the point of view of language theory. We show that in relation to the
``extended'' Chomsky hierarchy, the relevant computational model in the
unimodal case is the nested stack automaton or the related indexed languages,
while the bimodal case is modeled by the linear bounded automaton or the
related context-sensitive languages.Comment: 1 reference corrected, 1 reference added, minor changes in body of
manuscrip
School Mental Health in Charters: A Glimpse of Practitioners from a National Sample
Charter schools are part of a global push for alternative governance models in public education. Even though U.S. charter schools enroll nearly 3.2 million children, little is known about school mental health (SMH) practice in charter schools. The current study was the first step in a line of inquiry exploring SMH and school social work practice in charter schools. Using cross-sectional survey research methods, the authors conducted brief one-time phone surveys with charter school social workers and counselors identified using a stratified random sampling strategy with national charter school lists. The final sample for analysis was 473 schools. Of these, 44.4% (n = 210) had a school social worker or counselor present at least one day per week, of whom 67 (30.5%) were school social workers. The school social work sample reported a number of job titles, including “school social worker” (67%) and many (13.4%) that were a variation of counselor (e.g., “behavioral counselor,” “social emotional counselor”). Half were employed by their school, five were employed by an outside organization contracted with the school and eight were employed by the school’s chartering organization. More than three-quarters (83%) had a master\u27s degree in social work as their highest degree. Our findings provide a snapshot of the SMH and school social work workforce within the emerging practice setting of charter schools. Findings suggest that the SMH workforce may be professionally similar to those in traditional public schools, but with more flexibility for interprofessional collaboration, professional advocacy, and role definition. Other implications for research are also discussed
Introduction to focus issue: intrinsic and designed computation: information processing in dynamical systems-beyond the digital hegemony
How dynamical systems store and process information is a fundamental question that touches a remarkably wide set of contemporary issues: from the breakdown of Moore's scaling laws-that predicted the inexorable improvement in digital circuitry-to basic philosophical problems of pattern in the natural world. It is a question that also returns one to the earliest days of the foundations of dynamical systems theory, probability theory, mathematical logic, communication theory, and theoretical computer science. We introduce the broad and rather eclectic set of articles in this Focus Issue that highlights a range of current challenges in computing and dynamical systems
One-dimensional asymmetrically coupled maps with defects
In this letter we study chaotic dynamical properties of an asymmetrically
coupled one-dimensional chain of maps. We discuss the existence of coherent
regions in terms of the presence of defects along the chain. We find out that
temporal chaos is instantaneously localized around one single defect and that
the tangent vector jumps from one defect to another in an apparently random
way. We quantitatively measure the localization properties by defining an
entropy-like function in the space of tangent vectors.Comment: 9 pages + 4 figures TeX dialect: Plain TeX + IOP macros (included
On the influence of noise on chaos in nearly Hamiltonian systems
The simultaneous influence of small damping and white noise on Hamiltonian
systems with chaotic motion is studied on the model of periodically kicked
rotor. In the region of parameters where damping alone turns the motion into
regular, the level of noise that can restore the chaos is studied. This
restoration is created by two mechanisms: by fluctuation induced transfer of
the phase trajectory to domains of local instability, that can be described by
the averaging of the local instability index, and by destabilization of motion
within the islands of stability by fluctuation induced parametric modulation of
the stability matrix, that can be described by the methods developed in the
theory of Anderson localization in one-dimensional systems.Comment: 10 pages REVTEX, 9 figures EP
Local Causal States and Discrete Coherent Structures
Coherent structures form spontaneously in nonlinear spatiotemporal systems
and are found at all spatial scales in natural phenomena from laboratory
hydrodynamic flows and chemical reactions to ocean, atmosphere, and planetary
climate dynamics. Phenomenologically, they appear as key components that
organize the macroscopic behaviors in such systems. Despite a century of
effort, they have eluded rigorous analysis and empirical prediction, with
progress being made only recently. As a step in this, we present a formal
theory of coherent structures in fully-discrete dynamical field theories. It
builds on the notion of structure introduced by computational mechanics,
generalizing it to a local spatiotemporal setting. The analysis' main tool
employs the \localstates, which are used to uncover a system's hidden
spatiotemporal symmetries and which identify coherent structures as
spatially-localized deviations from those symmetries. The approach is
behavior-driven in the sense that it does not rely on directly analyzing
spatiotemporal equations of motion, rather it considers only the spatiotemporal
fields a system generates. As such, it offers an unsupervised approach to
discover and describe coherent structures. We illustrate the approach by
analyzing coherent structures generated by elementary cellular automata,
comparing the results with an earlier, dynamic-invariant-set approach that
decomposes fields into domains, particles, and particle interactions.Comment: 27 pages, 10 figures;
http://csc.ucdavis.edu/~cmg/compmech/pubs/dcs.ht
- …