146 research outputs found
The Political Economy of Unsustainable Fiscal Deficits
This paper uses an intertemporal model of public finances to show that political instability can cause taxes to be tilted to the future, resulting in a fiscal deficit that is suboptimal and only weakly sustainable (in the sense of Quintos). This occurs because political instability gives the government an incentive to implement a myopic fiscal policy in order to increase its chances of remaining in office. The government achieves this by delaying taxes (or advancing spending) in order to buy political support, which in turn causes an upward trend in the deficit process and a financial crisis. Using annual data for Chile for the 1833-1999 period, we present statistical test results that support the model.Fiscal policy, political instability, weak and strong sustainability, cointegration with change in regime
Statistical Complexity of Simple 1D Spin Systems
We present exact results for two complementary measures of spatial structure
generated by 1D spin systems with finite-range interactions. The first, excess
entropy, measures the apparent spatial memory stored in configurations. The
second, statistical complexity, measures the amount of memory needed to
optimally predict the chain of spin values. These statistics capture distinct
properties and are different from existing thermodynamic quantities.Comment: 4 pages with 2 eps Figures. Uses RevTeX macros. Also available at
http://www.santafe.edu/projects/CompMech/papers/CompMechCommun.htm
Prediction and Generation of Binary Markov Processes: Can a Finite-State Fox Catch a Markov Mouse?
Understanding the generative mechanism of a natural system is a vital
component of the scientific method. Here, we investigate one of the fundamental
steps toward this goal by presenting the minimal generator of an arbitrary
binary Markov process. This is a class of processes whose predictive model is
well known. Surprisingly, the generative model requires three distinct
topologies for different regions of parameter space. We show that a previously
proposed generator for a particular set of binary Markov processes is, in fact,
not minimal. Our results shed the first quantitative light on the relative
(minimal) costs of prediction and generation. We find, for instance, that the
difference between prediction and generation is maximized when the process is
approximately independently, identically distributed.Comment: 12 pages, 12 figures;
http://csc.ucdavis.edu/~cmg/compmech/pubs/gmc.ht
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
Quantum Mutual Information Capacity for High Dimensional Entangled States
High dimensional Hilbert spaces used for quantum communication channels offer
the possibility of large data transmission capabilities. We propose a method of
characterizing the channel capacity of an entangled photonic state in high
dimensional position and momentum bases. We use this method to measure the
channel capacity of a parametric downconversion state, achieving a channel
capacity over 7 bits/photon in either the position or momentum basis, by
measuring in up to 576 dimensions per detector. The channel violated an
entropic separability bound, suggesting the performance cannot be replicated
classically.Comment: 5 pages, 2 figure
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
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
Intrinsic Quantum Computation
We introduce ways to measure information storage in quantum systems, using a
recently introduced computation-theoretic model that accounts for measurement
effects. The first, the quantum excess entropy, quantifies the shared
information between a quantum process's past and its future. The second, the
quantum transient information, determines the difficulty with which an observer
comes to know the internal state of a quantum process through measurements. We
contrast these with von Neumann entropy and quantum entropy rate and provide a
closed-form expression for the latter for the class of deterministic quantum
processes.Comment: 5 pages, 1 figure, 1 table; updated with corrections;
http://cse.ucdavis.edu/~cmg/compmech/pubs/iqc.ht
Information Symmetries in Irreversible Processes
We study dynamical reversibility in stationary stochastic processes from an
information theoretic perspective. Extending earlier work on the reversibility
of Markov chains, we focus on finitary processes with arbitrarily long
conditional correlations. In particular, we examine stationary processes
represented or generated by edge-emitting, finite-state hidden Markov models.
Surprisingly, we find pervasive temporal asymmetries in the statistics of such
stationary processes with the consequence that the computational resources
necessary to generate a process in the forward and reverse temporal directions
are generally not the same. In fact, an exhaustive survey indicates that most
stationary processes are irreversible. We study the ensuing relations between
model topology in different representations, the process's statistical
properties, and its reversibility in detail. A process's temporal asymmetry is
efficiently captured using two canonical unifilar representations of the
generating model, the forward-time and reverse-time epsilon-machines. We
analyze example irreversible processes whose epsilon-machine presentations
change size under time reversal, including one which has a finite number of
recurrent causal states in one direction, but an infinite number in the
opposite. From the forward-time and reverse-time epsilon-machines, we are able
to construct a symmetrized, but nonunifilar, generator of a process---the
bidirectional machine. Using the bidirectional machine, we show how to directly
calculate a process's fundamental information properties, many of which are
otherwise only poorly approximated via process samples. The tools we introduce
and the insights we offer provide a better understanding of the many facets of
reversibility and irreversibility in stochastic processes.Comment: 32 pages, 17 figures, 2 tables;
http://csc.ucdavis.edu/~cmg/compmech/pubs/pratisp2.ht
Exact Synchronization for Finite-State Sources
We analyze how an observer synchronizes to the internal state of a
finite-state information source, using the epsilon-machine causal
representation. Here, we treat the case of exact synchronization, when it is
possible for the observer to synchronize completely after a finite number of
observations. The more difficult case of strictly asymptotic synchronization is
treated in a sequel. In both cases, we find that an observer, on average, will
synchronize to the source state exponentially fast and that, as a result, the
average accuracy in an observer's predictions of the source output approaches
its optimal level exponentially fast as well. Additionally, we show here how to
analytically calculate the synchronization rate for exact epsilon-machines and
provide an efficient polynomial-time algorithm to test epsilon-machines for
exactness.Comment: 9 pages, 6 figures; now includes analytical calculation of the
synchronization rate; updates and corrections adde
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