2,525 research outputs found
Dynamical complexity of discrete time regulatory networks
Genetic regulatory networks are usually modeled by systems of coupled
differential equations and by finite state models, better known as logical
networks, are also used. In this paper we consider a class of models of
regulatory networks which present both discrete and continuous aspects. Our
models consist of a network of units, whose states are quantified by a
continuous real variable. The state of each unit in the network evolves
according to a contractive transformation chosen from a finite collection of
possible transformations, according to a rule which depends on the state of the
neighboring units. As a first approximation to the complete description of the
dynamics of this networks we focus on a global characteristic, the dynamical
complexity, related to the proliferation of distinguishable temporal behaviors.
In this work we give explicit conditions under which explicit relations between
the topological structure of the regulatory network, and the growth rate of the
dynamical complexity can be established. We illustrate our results by means of
some biologically motivated examples.Comment: 28 pages, 4 figure
Quantifying hidden order out of equilibrium
While the equilibrium properties, states, and phase transitions of
interacting systems are well described by statistical mechanics, the lack of
suitable state parameters has hindered the understanding of non-equilibrium
phenomena in diverse settings, from glasses to driven systems to biology. The
length of a losslessly compressed data file is a direct measure of its
information content: The more ordered the data is, the lower its information
content and the shorter the length of its encoding can be made. Here, we
describe how data compression enables the quantification of order in
non-equilibrium and equilibrium many-body systems, both discrete and
continuous, even when the underlying form of order is unknown. We consider
absorbing state models on and off-lattice, as well as a system of active
Brownian particles undergoing motility-induced phase separation. The technique
reliably identifies non-equilibrium phase transitions, determines their
character, quantitatively predicts certain critical exponents without prior
knowledge of the order parameters, and reveals previously unknown ordering
phenomena. This technique should provide a quantitative measure of organization
in condensed matter and other systems exhibiting collective phase transitions
in and out of equilibrium
Predictability: a way to characterize Complexity
Different aspects of the predictability problem in dynamical systems are
reviewed. The deep relation among Lyapunov exponents, Kolmogorov-Sinai entropy,
Shannon entropy and algorithmic complexity is discussed. In particular, we
emphasize how a characterization of the unpredictability of a system gives a
measure of its complexity. Adopting this point of view, we review some
developments in the characterization of the predictability of systems showing
different kind of complexity: from low-dimensional systems to high-dimensional
ones with spatio-temporal chaos and to fully developed turbulence. A special
attention is devoted to finite-time and finite-resolution effects on
predictability, which can be accounted with suitable generalization of the
standard indicators. The problems involved in systems with intrinsic randomness
is discussed, with emphasis on the important problems of distinguishing chaos
from noise and of modeling the system. The characterization of irregular
behavior in systems with discrete phase space is also considered.Comment: 142 Latex pgs. 41 included eps figures, submitted to Physics Reports.
Related information at this http://axtnt2.phys.uniroma1.i
ANALYSIS OF SECURITY MEASURES FOR SEQUENCES
Stream ciphers are private key cryptosystems used for security in communication and data transmission systems. Because they are used to encrypt streams of data, it is necessary for stream ciphers to use primitives that are easy to implement and fast to operate. LFSRs and the recently invented FCSRs are two such primitives, which give rise to certain security measures for the cryptographic strength of sequences, which we refer to as complexity measures henceforth following the convention. The linear (resp. N-adic) complexity of a sequence is the length of the shortest LFSR (resp. FCSR) that can generate the sequence. Due to the availability of shift register synthesis algorithms, sequences used for cryptographic purposes should have high values for these complexity measures. It is also essential that the complexity of these sequences does not decrease when a few symbols are changed. The k-error complexity of a sequence is the smallest value of the complexity of a sequence obtained by altering k or fewer symbols in the given sequence. For a sequence to be considered cryptographically ‘strong’ it should have both high complexity and high error complexity values.
An important problem regarding sequence complexity measures is to determine good bounds on a specific complexity measure for a given sequence. In this thesis we derive new nontrivial lower bounds on the k-operation complexity of periodic sequences in both the linear and N-adic cases. Here the operations considered are combinations of insertions, deletions, and substitutions. We show that our bounds are tight and also derive several auxiliary results based on them.
A second problem on sequence complexity measures useful in the design and analysis of stream ciphers is to determine the number of sequences with a given fixed (error) complexity value. In this thesis we address this problem for the k-error linear complexity of 2n-periodic binary sequences. More specifically:
1. We characterize 2n-periodic binary sequences with fixed 2- or 3-error linear complexity and obtain the counting function for the number of such sequences with fixed k-error linear complexity for k = 2 or 3.
2. We obtain partial results on the number of 2n-periodic binary sequences with fixed k-error linear complexity when k is the minimum number of changes required to lower the linear complexity
Computation in Finitary Stochastic and Quantum Processes
We introduce stochastic and quantum finite-state transducers as
computation-theoretic models of classical stochastic and quantum finitary
processes. Formal process languages, representing the distribution over a
process's behaviors, are recognized and generated by suitable specializations.
We characterize and compare deterministic and nondeterministic versions,
summarizing their relative computational power in a hierarchy of finitary
process languages. Quantum finite-state transducers and generators are a first
step toward a computation-theoretic analysis of individual, repeatedly measured
quantum dynamical systems. They are explored via several physical systems,
including an iterated beam splitter, an atom in a magnetic field, and atoms in
an ion trap--a special case of which implements the Deutsch quantum algorithm.
We show that these systems' behaviors, and so their information processing
capacity, depends sensitively on the measurement protocol.Comment: 25 pages, 16 figures, 1 table; http://cse.ucdavis.edu/~cmg; numerous
corrections and update
Zero-temperature Monte Carlo study of the non-coplanar phase of the classical bilinear-biquadratic Heisenberg model on the triangular lattice
We investigate the ground-state properties of the highly degenerate
non-coplanar phase of the classical bilinear-biquadratic Heisenberg model on
the triangular lattice with Monte Carlo simulations. For that purpose, we
introduce an Ising pseudospin representation of the ground states, and we use a
simple Metropolis algorithm with local updates, as well as a powerful cluster
algorithm. At sizes that can be sampled with local updates, the presence of
long-range order is surprisingly combined with an algebraic decay of
correlations and the complete disordering of the chirality. It is only thanks
to the investigation of unusually large systems (containing spins)
with cluster updates that the true asymptotic regime can be reached and that
the system can be proven to consist of equivalent (i.e., equally ordered)
sublattices. These large-scale simulations also demonstrate that the scalar
chirality exhibits long-range order at zero temperature, implying that the
system has to undergo a finite-temperature phase transition. Finally, we show
that the average distance in the order parameter space, which has the structure
of an infinite Cayley tree, remains remarkably small between any pair of
points, even in the limit when the real space distance between them tends to
infinity.Comment: 15 pages, 10 figure
Reducing sequencing complexity in dynamical quantum error suppression by Walsh modulation
We study dynamical error suppression from the perspective of reducing
sequencing complexity, in order to facilitate efficient semi-autonomous
quantum-coherent systems. With this aim, we focus on digital sequences where
all interpulse time periods are integer multiples of a minimum clock period and
compatibility with simple digital classical control circuitry is intrinsic,
using so-called em Walsh functions as a general mathematical framework. The
Walsh functions are an orthonormal set of basis functions which may be
associated directly with the control propagator for a digital modulation
scheme, and dynamical decoupling (DD) sequences can be derived from the
locations of digital transitions therein. We characterize the suite of the
resulting Walsh dynamical decoupling (WDD) sequences, and identify the number
of periodic square-wave (Rademacher) functions required to generate a Walsh
function as the key determinant of the error-suppressing features of the
relevant WDD sequence. WDD forms a unifying theoretical framework as it
includes a large variety of well-known and novel DD sequences, providing
significant flexibility and performance benefits relative to basic
quasi-periodic design. We also show how Walsh modulation may be employed for
the protection of certain nontrivial logic gates, providing an implementation
of a dynamically corrected gate. Based on these insights we identify Walsh
modulation as a digital-efficient approach for physical-layer error
suppression.Comment: 15 pages, 3 figure
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