980 research outputs found
Prediction, Retrodiction, and The Amount of Information Stored in the Present
We introduce an ambidextrous view of stochastic dynamical systems, comparing
their forward-time and reverse-time representations and then integrating them
into a single time-symmetric representation. The perspective is useful
theoretically, computationally, and conceptually. Mathematically, we prove that
the excess entropy--a familiar measure of organization in complex systems--is
the mutual information not only between the past and future, but also between
the predictive and retrodictive causal states. Practically, we exploit the
connection between prediction and retrodiction to directly calculate the excess
entropy. Conceptually, these lead one to discover new system invariants for
stochastic dynamical systems: crypticity (information accessibility) and causal
irreversibility. Ultimately, we introduce a time-symmetric representation that
unifies all these quantities, compressing the two directional representations
into one. The resulting compression offers a new conception of the amount of
information stored in the present.Comment: 17 pages, 7 figures, 1 table;
http://users.cse.ucdavis.edu/~cmg/compmech/pubs/pratisp.ht
Information Accessibility and Cryptic Processes: Linear Combinations of Causal States
We show in detail how to determine the time-reversed representation of a
stationary hidden stochastic process from linear combinations of its
forward-time -machine causal states. This also gives a check for the
-cryptic expansion recently introduced to explore the temporal range over
which internal state information is spread.Comment: 6 pages, 9 figures, 2 tables;
http://users.cse.ucdavis.edu/~cmg/compmech/pubs/iacplcocs.ht
Invariant manifolds and the geometry of front propagation in fluid flows
Recent theoretical and experimental work has demonstrated the existence of
one-sided, invariant barriers to the propagation of reaction-diffusion fronts
in quasi-two-dimensional periodically-driven fluid flows. These barriers were
called burning invariant manifolds (BIMs). We provide a detailed theoretical
analysis of BIMs, providing criteria for their existence, a classification of
their stability, a formalization of their barrier property, and mechanisms by
which the barriers can be circumvented. This analysis assumes the sharp front
limit and negligible feedback of the front on the fluid velocity. A
low-dimensional dynamical systems analysis provides the core of our results.Comment: 14 pages, 11 figures. To appear in Chaos Focus Issue:
Chemo-Hydrodynamic Patterns and Instabilities (2012
Surveying structural complexity in quantum many-body systems
Quantum many-body systems exhibit a rich and diverse range of exotic
behaviours, owing to their underlying non-classical structure. These systems
present a deep structure beyond those that can be captured by measures of
correlation and entanglement alone. Using tools from complexity science, we
characterise such structure. We investigate the structural complexities that
can be found within the patterns that manifest from the observational data of
these systems. In particular, using two prototypical quantum many-body systems
as test cases - the one-dimensional quantum Ising and Bose-Hubbard models - we
explore how different information-theoretic measures of complexity are able to
identify different features of such patterns. This work furthers the
understanding of fully-quantum notions of structure and complexity in quantum
systems and dynamics.Comment: 9 pages, 5 figure
A protected area influences genotype-specific survival and the structure of a Canis hybrid zone
It is widely recognized that protected areas can strongly influence ecological systems and that hybridization is an important conservation issue. However, previous studies have not explicitly considered the influence of protected areas on hybridization dynamics. Eastern wolves are a species of special concern and their distribution is largely restricted to a protected population in Algonquin Provincial Park (APP), Ontario, Canada, where they are the numerically dominant canid. We studied intrinsic and extrinsic factors influencing survival and cause-specific mortality of hybrid and parental canids in the three-species hybrid zone between eastern wolves, eastern coyotes, and gray wolves in and adjacent to APP. Mortality risk for eastern wolves in areas adjacent to APP was significantly higher than for other sympatric Canis types outside of APP, and for eastern wolves and other canids within APP. Outside of APP, the annual mortality rate of all canids by harvest (24%) was higher than for other causes of death (4–7%). Furthermore, eastern wolves (hazard ratio ¼ 3.5) and nonresidents (transients and dispersing animals, hazard ratio ¼ 2.7) were more likely to die from harvest relative to other Canis types and residents, respectively. Thus, eastern wolves dispersing from APP were especially vulnerable to harvest mortality. For residents, eastern wolf survival was more negatively influenced by increased road density than for other Canis types, further highlighting the sensitivity of eastern wolves to human disturbance. A cycle of dispersal from APP followed by high rates of mortality and hybridization appears to maintain eastern wolves at low density adjacent to APP, limiting the potential for expansion beyond the protected area. However, high survival and numerical dominance of eastern wolves within APP suggest that protected areas can allow rare hybridizing species to persist even if their demographic performance is compromised and barriers to hybridization are largely absent in the adjacent matrix
Discussion of boundary-layer characteristics near the casing of an axial-flow compressor
Boundary-layer velocity profiles on the casing of an axial-flow compressor behind the guide vanes and rotor were measured and resolved into two components: along the streamline of the flow and perpendicular to it. Boundary-layer thickness and the deflection of the boundary layer at the wall were the generalizing parameters. By use of these results and the momentum-integral equations, the characteristics of boundary on the walls of axial-flow compressor are qualitatively discussed. Important parameters concerning secondary flow in the boundary layer appear to be turning of the flow and the product of boundary-layer thickness and streamline curvature outside the boundary layer. Two types of separation are shown to be possible in three dimensional boundary layer
Time's Barbed Arrow: Irreversibility, Crypticity, and Stored Information
We show why the amount of information communicated between the past and
future--the excess entropy--is not in general the amount of information stored
in the present--the statistical complexity. This is a puzzle, and a
long-standing one, since the latter is what is required for optimal prediction,
but the former describes observed behavior. We layout a classification scheme
for dynamical systems and stochastic processes that determines when these two
quantities are the same or different. We do this by developing closed-form
expressions for the excess entropy in terms of optimal causal predictors and
retrodictors--the epsilon-machines of computational mechanics. A process's
causal irreversibility and crypticity are key determining properties.Comment: 4 pages, 2 figure
Synchronization and Control in Intrinsic and Designed Computation: An Information-Theoretic Analysis of Competing Models of Stochastic Computation
We adapt tools from information theory to analyze how an observer comes to
synchronize with the hidden states of a finitary, stationary stochastic
process. We show that synchronization is determined by both the process's
internal organization and by an observer's model of it. We analyze these
components using the convergence of state-block and block-state entropies,
comparing them to the previously known convergence properties of the Shannon
block entropy. Along the way, we introduce a hierarchy of information
quantifiers as derivatives and integrals of these entropies, which parallels a
similar hierarchy introduced for block entropy. We also draw out the duality
between synchronization properties and a process's controllability. The tools
lead to a new classification of a process's alternative representations in
terms of minimality, synchronizability, and unifilarity.Comment: 25 pages, 13 figures, 1 tabl
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