3,062 research outputs found
Stability and convergence in discrete convex monotone dynamical systems
We study the stable behaviour of discrete dynamical systems where the map is
convex and monotone with respect to the standard positive cone. The notion of
tangential stability for fixed points and periodic points is introduced, which
is weaker than Lyapunov stability. Among others we show that the set of
tangentially stable fixed points is isomorphic to a convex inf-semilattice, and
a criterion is given for the existence of a unique tangentially stable fixed
point. We also show that periods of tangentially stable periodic points are
orders of permutations on letters, where is the dimension of the
underlying space, and a sufficient condition for global convergence to periodic
orbits is presented.Comment: 36 pages, 1 fugur
Quantum correlations and distinguishability of quantum states
A survey of various concepts in quantum information is given, with a main
emphasis on the distinguishability of quantum states and quantum correlations.
Covered topics include generalized and least square measurements, state
discrimination, quantum relative entropies, the Bures distance on the set of
quantum states, the quantum Fisher information, the quantum Chernoff bound,
bipartite entanglement, the quantum discord, and geometrical measures of
quantum correlations. The article is intended both for physicists interested
not only by collections of results but also by the mathematical methods
justifying them, and for mathematicians looking for an up-to-date introductory
course on these subjects, which are mainly developed in the physics literature.Comment: Review article, 103 pages, to appear in J. Math. Phys. 55 (special
issue: non-equilibrium statistical mechanics, 2014
The Causal Structure of Emotions in Aristotle: Hylomorphism, Causal Interaction between Mind and Body, and Intentionality
Recently, a strong hylomorphic reading of Aristotelian emotions has been put forward, one that allegedly eliminates the problem of causal interaction between soul and body. Taking the presentation of emotions in de An. I 1 as a starting point and basic thread, but relying also on the discussion of Rh. II, I will argue that this reading only takes into account two of the four causes of emotions, and that, if all four of them
are included into the picture, then a causal interaction of mind and body remains within Aristotelian emotions, independent of how strongly their hylomorphism is understood. Beyond the discussion with this recent reading, the analysis proposed of the fourfold causal structure of emotions is also intended as a hermeneutical starting point for a comprehensive analysis of particular emotions in Aristotle. Through the different causes Aristotle seems to account for many aspects of the complex phenomenon of emotion, including its physiological causes, its mental causes, and its intentional object
Cyclic projectors and separation theorems in idempotent convex geometry
Semimodules over idempotent semirings like the max-plus or tropical semiring
have much in common with convex cones. This analogy is particularly apparent in
the case of subsemimodules of the n-fold cartesian product of the max-plus
semiring it is known that one can separate a vector from a closed subsemimodule
that does not contain it. We establish here a more general separation theorem,
which applies to any finite collection of closed semimodules with a trivial
intersection. In order to prove this theorem, we investigate the spectral
properties of certain nonlinear operators called here idempotent cyclic
projectors. These are idempotent analogues of the cyclic nearest-point
projections known in convex analysis. The spectrum of idempotent cyclic
projectors is characterized in terms of a suitable extension of Hilbert's
projective metric. We deduce as a corollary of our main results the idempotent
analogue of Helly's theorem.Comment: 20 pages, 1 figur
Ruelle-Perron-Frobenius spectrum for Anosov maps
We extend a number of results from one dimensional dynamics based on spectral
properties of the Ruelle-Perron-Frobenius transfer operator to Anosov
diffeomorphisms on compact manifolds. This allows to develop a direct operator
approach to study ergodic properties of these maps. In particular, we show that
it is possible to define Banach spaces on which the transfer operator is
quasicompact. (Information on the existence of an SRB measure, its smoothness
properties and statistical properties readily follow from such a result.) In
dimension we show that the transfer operator associated to smooth random
perturbations of the map is close, in a proper sense, to the unperturbed
transfer operator. This allows to obtain easily very strong spectral stability
results, which in turn imply spectral stability results for smooth
deterministic perturbations as well. Finally, we are able to implement an Ulam
type finite rank approximation scheme thus reducing the study of the spectral
properties of the transfer operator to a finite dimensional problem.Comment: 58 pages, LaTe
Interdisciplinary Perspectives on Poverty Measurement, Epistemic Injustices and Social Activism
As we enter the 2020s, global poverty is still a grave and persistent problem.
Alleviating and eradicating poverty within and across the world’s societies
requires a thorough understanding of its nature and extent. Although economists
still standardly measure absolute and relative poverty in monetary terms, a consensus
is emerging that poverty is a socially relational problem involving deprivations
in multiple dimensions, including health, standard of living, education and political
participation. The anthology Dimensions of Poverty advances the interdisciplinary
debate on multidimensional poverty, and features contributions from leading international
experts and early career researchers (including from the Global South).
This introductory chapter gives an overview of formative debates, central concepts
and key findings. While monetary poverty measures are still dominant in public and
academic debate, their explanatory power has been drawn into question. We discuss
relevant criticisms before outlining the normative concepts that can inform both
multidimensional poverty and monetary measures, including basic capabilities,
basic needs and social primary goods. Next, we introduce several influential multidimensional
poverty indices, including the Human Development Index and the
Multidimensional Poverty Index. The anthology shows in detail how such measures
can be improved, from a variety of disciplinary perspectives. It shows that there are
different methods of poverty research that require further investigation, including
participatory studies, (value) surveys, public consensus building, the constitutional
approach, and financial diaries. Finally, we show that there is an ongoing problem
of epistemic asymmetries in global poverty research, and discuss responsibility for
addressing poverty, including the responsibilities of academics. The remainder of
the chapter is dedicated to a more detailed preview of the volume’s 20 contributions,
which are assembled along the following five themes: (I) poverty as a social relation;
(II) epistemic injustices in poverty research; (III) the social context of poverty;
(IV) measuring multidimensional poverty; and (V) country cases
Chaos and Synchronized Chaos in an Earthquake Model
We show that chaos is present in the symmetric two-block Burridge-Knopoff
model for earthquakes. This is in contrast with previous numerical studies, but
in agreement with experimental results. In this system, we have found a rich
dynamical behavior with an unusual route to chaos. In the three-block system,
we see the appearance of synchronized chaos, showing that this concept can have
potential applications in the field of seismology.Comment: To appear in Physical Review Letters (13 pages, 6 figures
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