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 $\epsilon$-machine causal states. This also gives a check for the $k$-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

Ordering block copolymers

A method for ordering block copolymers including forming a first layer having a first preference mode; and providing a reactive agent in selected regions of the first layer that modifies the selected regions to a second preference mode, wherein the selected regions define other regions of the first layer retaining the first preference mode thereby forming an alignment layer for block copolymers.Board of Regents, University of Texas Syste

Observations on the Ice-Breaking and Ice Navigation Behavior of Migrating Bowhead Whales (Balaena Mysticetus) near Point Barrow, Alaska, Spring 1985

During a four-day period from 28 April to 1 May 1985, we observed bowhead whales breaking up through sea ice in order to breathe. Our observations were made from grounded sea ice approximately 10 km northeast of Point Barrow, Alaska, during the spring bowhead migration (14 April to 10 June). From acoustic and visual data, it was estimated that 665 whales passed the observation perches during this four-day period. However, only 117(17%) whales were seen. The remaining whales either passed underneath the ice or were beyond the range of the visual observers. Whales used their heads, in the area of the blowholes, to push up against the ice (18 cm maximum thickness) and fracture it, creating a hummock of ice in which they were able to respire. Often during such breathing episodes, even at distances of only several hundred meters, the animal was not seen but its blows were clearly audible to the visual observers. Acoustic tracking of whales showed they avoided a large multi-year ice floe seaward of the observation perch. We hypothesize that bowheads use their calls to assess the thickness of ice in their migratory path. In assessing their calls, we suggest the whales can avoid areas where the ice is too thick to break through (to breath) and/or too thick to provide clearance for them to swim beneath.Key words: Balaena mysticetus, Point Barrow, bowhead whale, ice breaking, behavior, sea ice, singer, acoustic, anatomy, censusMots clés: Balaena mysticetus, Point Barrow, baleine franche, casser la glace, comportement, glace de mer, chanteuse, acoustique, anatomie, dénombremen

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

Anhydride copolymer top coats for orientation control of thin film block copolymers

The concepts described herein involve the use of random copolymer top coats that can be spin coated onto block copolymer thin films and used to control the interfacial energy of the top coat-block copolymer interface. The top coats are soluble in aqueous weak base and can change surface energy once they are deposited onto the block copolymer thin film. The use of self-assembled block copolymers to produce advanced lithographic patterns relies on their orientation control in thin films. Top coats potentially allow for the facile orientation control of block copolymers which would otherwise be quite challenging.Board of Regents, University of Texas Syste

Many Roads to Synchrony: Natural Time Scales and Their Algorithms

We consider two important time scales---the Markov and cryptic orders---that monitor how an observer synchronizes to a finitary stochastic process. We show how to compute these orders exactly and that they are most efficiently calculated from the epsilon-machine, a process's minimal unifilar model. Surprisingly, though the Markov order is a basic concept from stochastic process theory, it is not a probabilistic property of a process. Rather, it is a topological property and, moreover, it is not computable from any finite-state model other than the epsilon-machine. Via an exhaustive survey, we close by demonstrating that infinite Markov and infinite cryptic orders are a dominant feature in the space of finite-memory processes. We draw out the roles played in statistical mechanical spin systems by these two complementary length scales.Comment: 17 pages, 16 figures: http://cse.ucdavis.edu/~cmg/compmech/pubs/kro.htm. Santa Fe Institute Working Paper 10-11-02

Cosmic Ray Acceleration at the Forward Shock in Tycho's Supernova Remnant: Evidence from Chandra X-ray Observations

We present evidence for cosmic ray acceleration at the forward shock in Tycho's supernova remnant (SNR) from three X-ray observables: (1) the proximity of the contact discontinuity to the forward shock, or blast wave, (2) the morphology of the emission from the rim of Tycho, and (3) the spectral nature of the rim emission. We determine the locations of the blast wave (BW), contact discontinuity (CD), and reverse shock (RS) around the rim of Tycho's supernova remnant using a principal component analysis and other methods applied to new Chandra data. The azimuthal-angle-averaged radius of the BW is 251". For the CD and RS we find average radii of 241" and 183", respectively. Taking account of projection effects, we find ratios of 1:0.93:0.70 (BW:CD:RS). We show these values to be inconsistent with adiabatic hydrodynamical models of SNR evolution. The CD:BW ratio can be explained if cosmic ray acceleration of ions is occurring at the forward shock. The RS:BW ratio, as well as the strong Fe Ka emission from the Tycho ejecta, imply that the RS is not accelerating cosmic rays. We also extract radial profiles from ~34% of the rim of Tycho and compare them to models of surface brightness profiles behind the BW for a purely thermal plasma with an adiabatic shock. The observed morphology of the rim is much more strongly peaked than predicted by the model, indicating that such thermal emission is implausible here. Spectral analysis also implies that the rim emission is non-thermal in nature, lending further support to the idea that Tycho's forward shock is accelerating cosmic rays.Comment: 39 pages, 10 figures, accepted by Ap