330,125 research outputs found
Group entropies, correlation laws and zeta functions
The notion of group entropy is proposed. It enables to unify and generalize
many different definitions of entropy known in the literature, as those of
Boltzmann-Gibbs, Tsallis, Abe and Kaniadakis. Other new entropic functionals
are presented, related to nontrivial correlation laws characterizing
universality classes of systems out of equilibrium, when the dynamics is weakly
chaotic. The associated thermostatistics are discussed. The mathematical
structure underlying our construction is that of formal group theory, which
provides the general structure of the correlations among particles and dictates
the associated entropic functionals. As an example of application, the role of
group entropies in information theory is illustrated and generalizations of the
Kullback-Leibler divergence are proposed. A new connection between statistical
mechanics and zeta functions is established. In particular, Tsallis entropy is
related to the classical Riemann zeta function.Comment: to appear in Physical Review
Information theoretic treatment of tripartite systems and quantum channels
A Holevo measure is used to discuss how much information about a given POVM
on system is present in another system , and how this influences the
presence or absence of information about a different POVM on in a third
system . The main goal is to extend information theorems for mutually
unbiased bases or general bases to arbitrary POVMs, and especially to
generalize "all-or-nothing" theorems about information located in tripartite
systems to the case of \emph{partial information}, in the form of quantitative
inequalities. Some of the inequalities can be viewed as entropic uncertainty
relations that apply in the presence of quantum side information, as in recent
work by Berta et al. [Nature Physics 6, 659 (2010)]. All of the results also
apply to quantum channels: e.g., if \EC accurately transmits certain POVMs,
the complementary channel \FC will necessarily be noisy for certain other
POVMs. While the inequalities are valid for mixed states of tripartite systems,
restricting to pure states leads to the basis-invariance of the difference
between the information about contained in and .Comment: 21 pages. An earlier version of this paper attempted to prove our
main uncertainty relation, Theorem 5, using the achievability of the Holevo
quantity in a coding task, an approach that ultimately failed because it did
not account for locking of classical correlations, e.g. see [DiVincenzo et
al. PRL. 92, 067902 (2004)]. In the latest version, we use a very different
approach to prove Theorem
A moment-matching Ferguson and Klass algorithm
Completely random measures (CRM) represent the key building block of a wide
variety of popular stochastic models and play a pivotal role in modern Bayesian
Nonparametrics. A popular representation of CRMs as a random series with
decreasing jumps is due to Ferguson and Klass (1972). This can immediately be
turned into an algorithm for sampling realizations of CRMs or more elaborate
models involving transformed CRMs. However, concrete implementation requires to
truncate the random series at some threshold resulting in an approximation
error. The goal of this paper is to quantify the quality of the approximation
by a moment-matching criterion, which consists in evaluating a measure of
discrepancy between actual moments and moments based on the simulation output.
Seen as a function of the truncation level, the methodology can be used to
determine the truncation level needed to reach a certain level of precision.
The resulting moment-matching \FK algorithm is then implemented and illustrated
on several popular Bayesian nonparametric models.Comment: 24 pages, 6 figures, 5 table
Additivity and non-additivity of multipartite entanglement measures
We study the additivity property of three multipartite entanglement measures,
i.e. the geometric measure of entanglement (GM), the relative entropy of
entanglement and the logarithmic global robustness. First, we show the
additivity of GM of multipartite states with real and non-negative entries in
the computational basis. Many states of experimental and theoretical interests
have this property, e.g. Bell diagonal states, maximally correlated generalized
Bell diagonal states, generalized Dicke states, the Smolin state, and the
generalization of D\"{u}r's multipartite bound entangled states. We also prove
the additivity of other two measures for some of these examples. Second, we
show the non-additivity of GM of all antisymmetric states of three or more
parties, and provide a unified explanation of the non-additivity of the three
measures of the antisymmetric projector states. In particular, we derive
analytical formulae of the three measures of one copy and two copies of the
antisymmetric projector states respectively. Third, we show, with a statistical
approach, that almost all multipartite pure states with sufficiently large
number of parties are nearly maximally entangled with respect to GM and
relative entropy of entanglement. However, their GM is not strong additive;
what's more surprising, for generic pure states with real entries in the
computational basis, GM of one copy and two copies, respectively, are almost
equal. Hence, more states may be suitable for universal quantum computation, if
measurements can be performed on two copies of the resource states. We also
show that almost all multipartite pure states cannot be produced reversibly
with the combination multipartite GHZ states under asymptotic LOCC, unless
relative entropy of entanglement is non-additive for generic multipartite pure
states.Comment: 45 pages, 4 figures. Proposition 23 and Theorem 24 are revised by
correcting a minor error from Eq. (A.2), (A.3) and (A.4) in the published
version. The abstract, introduction, and summary are also revised. All other
conclusions are unchange
Using individual tracking data to validate the predictions of species distribution models
The authors would like to thank the College of Life Sciences of Aberdeen University and Marine Scotland Science which funded CP's PhD project. Skate tagging experiments were undertaken as part of Scottish Government project SP004. We thank Ian Burrett for help in catching the fish and the other fishermen and anglers who returned tags. We thank José Manuel Gonzalez-Irusta for extracting and making available the environmental layers used as environmental covariates in the environmental suitability modelling procedure. We also thank Jason Matthiopoulos for insightful suggestions on habitat utilization metrics as well as Stephen C.F. Palmer, and three anonymous reviewers for useful suggestions to improve the clarity and quality of the manuscript.Peer reviewedPostprintPostprintPostprintPostprintPostprin
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