148,855 research outputs found
A categorical semantics for causal structure
We present a categorical construction for modelling causal structures within
a general class of process theories that include the theory of classical
probabilistic processes as well as quantum theory. Unlike prior constructions
within categorical quantum mechanics, the objects of this theory encode
fine-grained causal relationships between subsystems and give a new method for
expressing and deriving consequences for a broad class of causal structures. We
show that this framework enables one to define families of processes which are
consistent with arbitrary acyclic causal orderings. In particular, one can
define one-way signalling (a.k.a. semi-causal) processes, non-signalling
processes, and quantum -combs. Furthermore, our framework is general enough
to accommodate recently-proposed generalisations of classical and quantum
theory where processes only need to have a fixed causal ordering locally, but
globally allow indefinite causal ordering.
To illustrate this point, we show that certain processes of this kind, such
as the quantum switch, the process matrices of Oreshkov, Costa, and Brukner,
and a classical three-party example due to Baumeler, Feix, and Wolf are all
instances of a certain family of processes we refer to as in
the appropriate category of higher-order causal processes. After defining these
families of causal structures within our framework, we give derivations of
their operational behaviour using simple, diagrammatic axioms.Comment: Extended version of a LICS 2017 paper with the same titl
The age of information in gossip networks
We introduce models of gossip based communication networks in which each node
is simultaneously a sensor, a relay and a user of information. We model the
status of ages of information between nodes as a discrete time Markov chain. In
this setting a gossip transmission policy is a decision made at each node
regarding what type of information to relay at any given time (if any). When
transmission policies are based on random decisions, we are able to analyze the
age of information in certain illustrative structured examples either by means
of an explicit analysis, an algorithm or asymptotic approximations. Our key
contribution is presenting this class of models.Comment: 15 pages, 8 figure
A quantum causal discovery algorithm
Finding a causal model for a set of classical variables is now a
well-established task---but what about the quantum equivalent? Even the notion
of a quantum causal model is controversial. Here, we present a causal discovery
algorithm for quantum systems. The input to the algorithm is a process matrix
describing correlations between quantum events. Its output consists of
different levels of information about the underlying causal model. Our
algorithm determines whether the process is causally ordered by grouping the
events into causally-ordered non-signaling sets. It detects if all relevant
common causes are included in the process, which we label Markovian, or
alternatively if some causal relations are mediated through some external
memory. For a Markovian process, it outputs a causal model, namely the causal
relations and the corresponding mechanisms, represented as quantum states and
channels. Our algorithm provides a first step towards more general methods for
quantum causal discovery.Comment: 11 pages, 10 figures, revised to match published versio
On directed information theory and Granger causality graphs
Directed information theory deals with communication channels with feedback.
When applied to networks, a natural extension based on causal conditioning is
needed. We show here that measures built from directed information theory in
networks can be used to assess Granger causality graphs of stochastic
processes. We show that directed information theory includes measures such as
the transfer entropy, and that it is the adequate information theoretic
framework needed for neuroscience applications, such as connectivity inference
problems.Comment: accepted for publications, Journal of Computational Neuroscienc
Cooperative surmounting of bottlenecks
The physics of activated escape of objects out of a metastable state plays a
key role in diverse scientific areas involving chemical kinetics, diffusion and
dislocation motion in solids, nucleation, electrical transport, motion of flux
lines superconductors, charge density waves, and transport processes of
macromolecules, to name but a few. The underlying activated processes present
the multidimensional extension of the Kramers problem of a single Brownian
particle. In comparison to the latter case, however, the dynamics ensuing from
the interactions of many coupled units can lead to intriguing novel phenomena
that are not present when only a single degree of freedom is involved. In this
review we report on a variety of such phenomena that are exhibited by systems
consisting of chains of interacting units in the presence of potential
barriers.
In the first part we consider recent developments in the case of a
deterministic dynamics driving cooperative escape processes of coupled
nonlinear units out of metastable states. The ability of chains of coupled
units to undergo spontaneous conformational transitions can lead to a
self-organised escape. The mechanism at work is that the energies of the units
become re-arranged, while keeping the total energy conserved, in forming
localised energy modes that in turn trigger the cooperative escape. We present
scenarios of significantly enhanced noise-free escape rates if compared to the
noise-assisted case.
The second part deals with the collective directed transport of systems of
interacting particles overcoming energetic barriers in periodic potential
landscapes. Escape processes in both time-homogeneous and time-dependent driven
systems are considered for the emergence of directed motion. It is shown that
ballistic channels immersed in the associated high-dimensional phase space are
the source for the directed long-range transport
- …