194,547 research outputs found
Local information transfer as a spatiotemporal filter for complex systems
We present a measure of local information transfer, derived from an existing
averaged information-theoretical measure, namely transfer entropy. Local
transfer entropy is used to produce profiles of the information transfer into
each spatiotemporal point in a complex system. These spatiotemporal profiles
are useful not only as an analytical tool, but also allow explicit
investigation of different parameter settings and forms of the transfer entropy
metric itself. As an example, local transfer entropy is applied to cellular
automata, where it is demonstrated to be a novel method of filtering for
coherent structure. More importantly, local transfer entropy provides the first
quantitative evidence for the long-held conjecture that the emergent traveling
coherent structures known as particles (both gliders and domain walls, which
have analogues in many physical processes) are the dominant information
transfer agents in cellular automata.Comment: 12 page
Transfer Entropy as a Log-likelihood Ratio
Transfer entropy, an information-theoretic measure of time-directed
information transfer between joint processes, has steadily gained popularity in
the analysis of complex stochastic dynamics in diverse fields, including the
neurosciences, ecology, climatology and econometrics. We show that for a broad
class of predictive models, the log-likelihood ratio test statistic for the
null hypothesis of zero transfer entropy is a consistent estimator for the
transfer entropy itself. For finite Markov chains, furthermore, no explicit
model is required. In the general case, an asymptotic chi-squared distribution
is established for the transfer entropy estimator. The result generalises the
equivalence in the Gaussian case of transfer entropy and Granger causality, a
statistical notion of causal influence based on prediction via vector
autoregression, and establishes a fundamental connection between directed
information transfer and causality in the Wiener-Granger sense
Permutation Complexity and Coupling Measures in Hidden Markov Models
In [Haruna, T. and Nakajima, K., 2011. Physica D 240, 1370-1377], the authors
introduced the duality between values (words) and orderings (permutations) as a
basis to discuss the relationship between information theoretic measures for
finite-alphabet stationary stochastic processes and their permutation
analogues. It has been used to give a simple proof of the equality between the
entropy rate and the permutation entropy rate for any finite-alphabet
stationary stochastic process and show some results on the excess entropy and
the transfer entropy for finite-alphabet stationary ergodic Markov processes.
In this paper, we extend our previous results to hidden Markov models and show
the equalities between various information theoretic complexity and coupling
measures and their permutation analogues. In particular, we show the following
two results within the realm of hidden Markov models with ergodic internal
processes: the two permutation analogues of the transfer entropy, the symbolic
transfer entropy and the transfer entropy on rank vectors, are both equivalent
to the transfer entropy if they are considered as the rates, and the directed
information theory can be captured by the permutation entropy approach.Comment: 26 page
Symbolic transfer entropy rate is equal to transfer entropy rate for bivariate finite-alphabet stationary ergodic Markov processes
Transfer entropy is a measure of the magnitude and the direction of
information flow between jointly distributed stochastic processes. In recent
years, its permutation analogues are considered in the literature to estimate
the transfer entropy by counting the number of occurrences of orderings of
values, not the values themselves. It has been suggested that the method of
permutation is easy to implement, computationally low cost and robust to noise
when applying to real world time series data. In this paper, we initiate a
theoretical treatment of the corresponding rates. In particular, we consider
the transfer entropy rate and its permutation analogue, the symbolic transfer
entropy rate, and show that they are equal for any bivariate finite-alphabet
stationary ergodic Markov process. This result is an illustration of the
duality method introduced in [T. Haruna and K. Nakajima, Physica D 240, 1370
(2011)]. We also discuss the relationship among the transfer entropy rate, the
time-delayed mutual information rate and their permutation analogues.Comment: 18 page
Information transfer in signaling pathways : a study using coupled simulated and experimental data
Background: The topology of signaling cascades has been studied in quite some detail. However, how information is processed exactly is still relatively unknown. Since quite diverse information has to be transported by one and the same signaling cascade (e.g. in case of different agonists), it is clear that the underlying mechanism is more complex than a simple binary switch which relies on the
mere presence or absence of a particular species. Therefore, finding means to analyze the information transferred will help in deciphering how information is processed exactly in the cell. Using the information-theoretic measure transfer entropy, we studied the properties of information transfer in an example case, namely calcium signaling under different cellular
conditions. Transfer entropy is an asymmetric and dynamic measure of the dependence of two (nonlinear) stochastic processes. We used calcium signaling since it is a well-studied example of complex cellular signaling. It has been suggested that specific information is encoded in the
amplitude, frequency and waveform of the oscillatory Ca2+-signal.
Results: We set up a computational framework to study information transfer, e.g. for calcium
signaling at different levels of activation and different particle numbers in the system. We stochastically coupled simulated and experimentally measured calcium signals to simulated target proteins and used kernel density methods to estimate the transfer entropy from these bivariate
time series. We found that, most of the time, the transfer entropy increases with increasing particle numbers. In systems with only few particles, faithful information transfer is hampered by random fluctuations. The transfer entropy also seems to be slightly correlated to the complexity (spiking, bursting or irregular oscillations) of the signal. Finally, we discuss a number of peculiarities of our approach in detail.
Conclusion: This study presents the first application of transfer entropy to biochemical signaling pathways. We could quantify the information transferred from simulated/experimentally measured calcium signals to a target enzyme under different cellular conditions. Our approach, comprising stochastic coupling and using the information-theoretic measure transfer entropy, could also be a valuable tool for the analysis of other signaling pathways
Information transfer in signaling pathways : a study using coupled simulated and experimental data
Background: The topology of signaling cascades has been studied in quite some detail. However, how information is processed exactly is still relatively unknown. Since quite diverse information has to be transported by one and the same signaling cascade (e.g. in case of different agonists), it is clear that the underlying mechanism is more complex than a simple binary switch which relies on the
mere presence or absence of a particular species. Therefore, finding means to analyze the information transferred will help in deciphering how information is processed exactly in the cell. Using the information-theoretic measure transfer entropy, we studied the properties of information transfer in an example case, namely calcium signaling under different cellular
conditions. Transfer entropy is an asymmetric and dynamic measure of the dependence of two (nonlinear) stochastic processes. We used calcium signaling since it is a well-studied example of complex cellular signaling. It has been suggested that specific information is encoded in the
amplitude, frequency and waveform of the oscillatory Ca2+-signal.
Results: We set up a computational framework to study information transfer, e.g. for calcium
signaling at different levels of activation and different particle numbers in the system. We stochastically coupled simulated and experimentally measured calcium signals to simulated target proteins and used kernel density methods to estimate the transfer entropy from these bivariate
time series. We found that, most of the time, the transfer entropy increases with increasing particle numbers. In systems with only few particles, faithful information transfer is hampered by random fluctuations. The transfer entropy also seems to be slightly correlated to the complexity (spiking, bursting or irregular oscillations) of the signal. Finally, we discuss a number of peculiarities of our approach in detail.
Conclusion: This study presents the first application of transfer entropy to biochemical signaling pathways. We could quantify the information transferred from simulated/experimentally measured calcium signals to a target enzyme under different cellular conditions. Our approach, comprising stochastic coupling and using the information-theoretic measure transfer entropy, could also be a valuable tool for the analysis of other signaling pathways
Exact Entanglement dynamics in Three Interacting Qubits
Motivated by recent experimental study on coherent dynamics transfer in three
interacting atoms or electron spins \cite{Barredo:2015,Rosenfeld:2018}, here we
study entanglement entropy transfer in three interacting qubits. We
analytically calculate time evolutions of wave function, density matrix and
entanglement of the system. We find that initially entangled two qubits may
alternatively transfer their entanglement entropy to other two qubit pairs. So
that dynamical evolution of three interacting qubits may produce a genuine
three-partite entangled state through entanglement entropy transfers. In
particular, different pairwise interactions of the three qubits endow symmetric
and asymmetric evolutions of the entanglement transfer, characterized by the
quantum mutual information and concurence. Finally, we discuss an experimental
proposal of three Rydberg atoms for testing the entanglement dynamics transfer
of this kind.Comment: 6 pages + 5 figure
The limit behavior of the evolution of Tsallis entropy in self-gravitating systems
In this letter, we study the limit behavior of the evolution of Tsallis
entropy in self-gravitating systems. The study is carried out under two
different situations, drawing the same conclusion. No matter in the energy
transfer process or in the mass transfer process inside the system, when
nonextensive parameter q is more than unity, the total entropy is bounded; on
the contrary, when this parameter is less than unity, the total entropy is
unbounded. There are proofs in both theory and observation that the q is always
more than unity. So the Tsallis entropy in self-gravitating system generally
exhibits a bounded property. This indicates the existence of global maximum of
Tsallis entropy. It is possible for self-gravitating systems to evolve to
thermodynamically stable states
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