17,432 research outputs found
Occam's Quantum Strop: Synchronizing and Compressing Classical Cryptic Processes via a Quantum Channel
A stochastic process's statistical complexity stands out as a fundamental
property: the minimum information required to synchronize one process generator
to another. How much information is required, though, when synchronizing over a
quantum channel? Recent work demonstrated that representing causal similarity
as quantum state-indistinguishability provides a quantum advantage. We
generalize this to synchronization and offer a sequence of constructions that
exploit extended causal structures, finding substantial increase of the quantum
advantage. We demonstrate that maximum compression is determined by the
process's cryptic order---a classical, topological property closely allied to
Markov order, itself a measure of historical dependence. We introduce an
efficient algorithm that computes the quantum advantage and close noting that
the advantage comes at a cost---one trades off prediction for generation
complexity.Comment: 10 pages, 6 figures;
http://csc.ucdavis.edu/~cmg/compmech/pubs/oqs.ht
Information measure for financial time series: quantifying short-term market heterogeneity
A well-interpretable measure of information has been recently proposed based
on a partition obtained by intersecting a random sequence with its moving
average. The partition yields disjoint sets of the sequence, which are then
ranked according to their size to form a probability distribution function and
finally fed in the expression of the Shannon entropy. In this work, such
entropy measure is implemented on the time series of prices and volatilities of
six financial markets. The analysis has been performed, on tick-by-tick data
sampled every minute for six years of data from 1999 to 2004, for a broad range
of moving average windows and volatility horizons. The study shows that the
entropy of the volatility series depends on the individual market, while the
entropy of the price series is practically a market-invariant for the six
markets. Finally, a cumulative information measure - the `Market Heterogeneity
Index'- is derived from the integral of the proposed entropy measure. The
values of the Market Heterogeneity Index are discussed as possible tools for
optimal portfolio construction and compared with those obtained by using the
Sharpe ratio a traditional risk diversity measure
Golden Ratio Versus Pi as Random Sequence Sources for Monte Carlo Integration
We discuss here the relative merits of these numbers as possible random sequence sources. The quality of these sequences is not judged directly based on the outcome of all known tests for the randomness of a sequence. Instead, it is determined implicitly by the accuracy of the Monte Carlo integration in a statistical sense. Since our main motive of using a random sequence is to solve real world problems, it is more desirable if we compare the quality of the sequences based on their performances for these problems in terms of quality/accuracy of the output. We also compare these sources against those generated by a popular pseudo-random generator, viz., the Matlab rand and the quasi-random generator ha/ton both in terms of error and time complexity. Our study demonstrates that consecutive blocks of digits of each of these numbers produce a good random sequence source. It is observed that randomly chosen blocks of digits do not have any remarkable advantage over consecutive blocks for the accuracy of the Monte Carlo integration. Also, it reveals that pi is a better source of a random sequence than theta when the accuracy of the integration is concerned
Numerical investigations of discrete scale invariance in fractals and multifractal measures
Fractals and multifractals and their associated scaling laws provide a
quantification of the complexity of a variety of scale invariant complex
systems. Here, we focus on lattice multifractals which exhibit complex
exponents associated with observable log-periodicity. We perform detailed
numerical analyses of lattice multifractals and explain the origin of three
different scaling regions found in the moments. A novel numerical approach is
proposed to extract the log-frequencies. In the non-lattice case, there is no
visible log-periodicity, {\em{i.e.}}, no preferred scaling ratio since the set
of complex exponents spread irregularly within the complex plane. A non-lattice
multifractal can be approximated by a sequence of lattice multifractals so that
the sets of complex exponents of the lattice sequence converge to the set of
complex exponents of the non-lattice one. An algorithm for the construction of
the lattice sequence is proposed explicitly.Comment: 31 Elsart pages including 12 eps figure
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