19 research outputs found
Complex Networks from Classical to Quantum
Recent progress in applying complex network theory to problems in quantum
information has resulted in a beneficial crossover. Complex network methods
have successfully been applied to transport and entanglement models while
information physics is setting the stage for a theory of complex systems with
quantum information-inspired methods. Novel quantum induced effects have been
predicted in random graphs---where edges represent entangled links---and
quantum computer algorithms have been proposed to offer enhancement for several
network problems. Here we review the results at the cutting edge, pinpointing
the similarities and the differences found at the intersection of these two
fields.Comment: 12 pages, 4 figures, REVTeX 4-1, accepted versio
Entrograms and coarse graining of dynamics on complex networks
Using an information theoretic point of view, we investigate how a dynamics
acting on a network can be coarse grained through the use of graph partitions.
Specifically, we are interested in how aggregating the state space of a Markov
process according to a partition impacts on the thus obtained lower-dimensional
dynamics. We highlight that for a dynamics on a particular graph there may be
multiple coarse grained descriptions that capture different, incomparable
features of the original process. For instance, a coarse graining induced by
one partition may be commensurate with a time-scale separation in the dynamics,
while another coarse graining may correspond to a different lower-dimensional
dynamics that preserves the Markov property of the original process. Taking
inspiration from the literature of Computational Mechanics, we find that a
convenient tool to summarise and visualise such dynamical properties of a
coarse grained model (partition) is the entrogram. The entrogram gathers
certain information-theoretic measures, which quantify how information flows
across time steps. These information theoretic quantities include the entropy
rate, as well as a measure for the memory contained in the process, i.e., how
well the dynamics can be approximated by a first order Markov process. We use
the entrogram to investigate how specific macro-scale connection patterns in
the state-space transition graph of the original dynamics result in desirable
properties of coarse grained descriptions. We thereby provide a fresh
perspective on the interplay between structure and dynamics in networks, and
the process of partitioning from an information theoretic perspective. We focus
on networks that may be approximated by both a core-periphery or a clustered
organization, and highlight that each of these coarse grained descriptions can
capture different aspects of a Markov process acting on the network.Comment: 17 pages, 6 figue
Analysis of the Equilibrium and Kinetics of the Ankyrin Repeat Protein Myotrophin
We apply the Wako-Saito-Munoz-Eaton model to the study of Myotrophin, a small
ankyrin repeat protein, whose folding equilibrium and kinetics have been
recently characterized experimentally. The model, which is a native-centric
with binary variables, provides a finer microscopic detail than the Ising
model, that has been recently applied to some different repeat proteins, while
being still amenable for an exact solution. In partial agreement with the
experiments, our results reveal a weakly three-state equilibrium and a
two-state-like kinetics of the wild type protein despite the presence of a
non-trivial free-energy profile. These features appear to be related to a
careful "design" of the free-energy landscape, so that mutations can alter this
picture, stabilizing some intermediates and changing the position of the
rate-limiting step. Also the experimental findings of two alternative pathways,
an N-terminal and a C-terminal one, are qualitatively confirmed, even if the
variations in the rates upon the experimental mutations cannot be
quantitatively reproduced. Interestingly, folding and unfolding pathway appear
to be different, even if closely related: a property that is not generally
considered in the phenomenological interpretation of the experimental data.Comment: 27 pages, 7 figure
Quantum Transport Enhancement by Time-Reversal Symmetry Breaking
Quantum mechanics still provides new unexpected effects when considering the
transport of energy and information. Models of continuous time quantum walks,
which implicitly use time-reversal symmetric Hamiltonians, have been intensely
used to investigate the effectiveness of transport. Here we show how breaking
time-reversal symmetry of the unitary dynamics in this model can enable
directional control, enhancement, and suppression of quantum transport.
Examples ranging from exciton transport to complex networks are presented. This
opens new prospects for more efficient methods to transport energy and
information.Comment: 6+5 page
Community Detection in Quantum Complex Networks
Determining community structure is a central topic in the study of complex
networks, be it technological, social, biological or chemical, in static or
interacting systems. In this paper, we extend the concept of community
detection from classical to quantum systems---a crucial missing component of a
theory of complex networks based on quantum mechanics. We demonstrate that
certain quantum mechanical effects cannot be captured using current classical
complex network tools and provide new methods that overcome these problems. Our
approaches are based on defining closeness measures between nodes, and then
maximizing modularity with hierarchical clustering. Our closeness functions are
based on quantum transport probability and state fidelity, two important
quantities in quantum information theory. To illustrate the effectiveness of
our approach in detecting community structure in quantum systems, we provide
several examples, including a naturally occurring light-harvesting complex,
LHCII. The prediction of our simplest algorithm, semiclassical in nature,
mostly agrees with a proposed partitioning for the LHCII found in quantum
chemistry literature, whereas our fully quantum treatment of the problem
uncovers a new, consistent, and appropriately quantum community structure.Comment: 16 pages, 4 figures, 1 tabl
Chiral Quantum Walks
Given its importance to many other areas of physics, from condensed matter
physics to thermodynamics, time-reversal symmetry has had relatively little
influence on quantum information science. Here we develop a network-based
picture of time-reversal theory, classifying Hamiltonians and quantum circuits
as time-symmetric or not in terms of the elements and geometries of their
underlying networks. Many of the typical circuits of quantum information
science are found to exhibit time-asymmetry. Moreover, we show that
time-asymmetry in circuits can be controlled using local gates only, and can
simulate time-asymmetry in Hamiltonian evolution. We experimentally implement a
fundamental example in which controlled time-reversal asymmetry in a
palindromic quantum circuit leads to near-perfect transport. Our results pave
the way for using time-symmetry breaking to control coherent transport, and
imply that time-asymmetry represents an omnipresent yet poorly understood
effect in quantum information science.Comment: 9 pages, 4 figures, REVTeX 4.1 - published versio
Measuring dynamical systems on directed hyper-graphs
Networks and graphs provide a simple but effective model to a vast set of
systems which building blocks interact throughout pairwise interactions.
Unfortunately, such models fail to describe all those systems which building
blocks interact at a higher order. Higher order graphs provide us the right
tools for the task, but introduce a higher computing complexity due to the
interaction order. In this paper we analyze the interplay between the structure
of a directed hypergraph and a linear dynamical system, a random walk, evolving
on it. How can one extend network measures, such as centrality or modularity,
to this framework? Instead of redefining network measures through the
hypergraph framework, with the consequent complexity boost, we will measure the
dynamical system associated to it. This approach let us apply known measures to
pairwise structures, such as the transition matrix, and determine a family of
measures that are amenable of such procedure.Comment: 8 pages, 5 figure
MS/MS Spectra Interpretation as a Statistical–Mechanics Problem
We describe a new method for peptide
sequencing based on the mapping
of the interpretation of tandem mass spectra onto the analysis of
the equilibrium distribution of a suitably defined physical model,
whose variables describe the positions of the fragmentation sites
along a discrete mass index. The model is governed by a potential
energy function that, at present, we derive ad hoc from the distribution
of peaks in a data set of experimental spectra. The statistical–physics
perspective prompts for a consistent and unified approach to de novo
and database-search methods, which is a distinctive feature of this
approach over alternative ones: the characterization of the ground
state of the model allows the de novo identification of the precursor
peptide; the study of the thermodynamic variables as a function of
the (fictitious) temperature gives insight on the quality of the prediction,
while the probability profiles at nonzero temperature reveal, on one
hand, which fragments are more reliably predicted. On the other hand,
they can be used as a spectrum-adapted, a posteriori score for database
search. Results obtained with two different test data sets reveal
a performance similar to that of other de novo and database-search
methods, which is reasonable, given the lack of an aggressive optimization
of the energy function at this stage. An important feature of the
method is that it is quite general and can be applied with different
choices of the energy function: we discuss its possible improvements
and generalizations
State Aggregations in Markov Chains and Block Models of Networks
We consider state-aggregation schemes for Markov chains from an information-theoretic perspective. Specifically, we consider aggregating the states of a Markov chain such that the mutual information of the aggregated states separated by T time steps is maximized. We show that for T ¼ 1 this recovers the maximum-likelihood estimator of the degree-corrected stochastic block model as a particular case, which enables us to explain certain features of the likelihood landscape of this generative network model from a dynamical lens. We further highlight how we can uncover coherent, long-range dynamical modules for which considering a timescale T ≫ 1 is essential. We demonstrate our results using synthetic flows and real-world ocean currents, where we are able to recover the fundamental features of the surface currents of the oceans
Assessing the influence of French vaccine critics during the two first years of the COVID-19 pandemic
International audienceWhen the threat of COVID-19 became widely acknowledged, many hoped that this pandemic would squash “the anti-vaccine movement”. However, when vaccines started arriving in rich countries at the end of 2020, it appeared that vaccine hesitancy might be an issue even in the context of this major pandemic. Does it mean that the mobilization of vaccine-critical activists on social media is one of the main causes of this reticence to vaccinate against COVID-19? In this paper, we wish to contribute to current work on vaccine hesitancy during the COVID-19 pandemic by looking at one of the many mechanisms which can cause reticence towards vaccines: the capacity of vaccine-critical activists to influence a wider public on social media. We analyze the evolution of debates over the COVID-19 vaccine on the French Twittosphere, during two first years of the pandemic, with a particular attention to the spreading capacity of vaccine-critical websites. We address two main questions: 1) Did vaccine-critical contents gain ground during this period? 2) Who were the main actors in the diffusion of these contents? While debates over vaccines experienced a tremendous surge during this period, the share of vaccine-critical contents in these debates remains stable except for a limited number of short periods associated with specific events. Secondly, analyzing the community structure of the re-tweets hyper-graph, we reconstruct the mesoscale structure of the information flows, identifying and characterizing the major communities of users. We analyze their role in the information ecosystem: the largest right-wing community has a typical echo-chamber behavior collecting all the vaccine-critical tweets from outside and recirculating it inside the community. The smaller left-wing community is less permeable to vaccine-critical contents but, has a large capacity to spread it once adopted