261 research outputs found
A fresh look on economic evolution from kinetic viewpoint
The present paper makes a contribution to fill in a gap left open by dynamic theory and evolutionary economics as well. While the "closed loop" dynamic theory has explanation power in analyzing evolving economic systems at the price of neglecting the possible occurrence of non anticipated novelties, "open loop" evolutionary economics is subject to the converse trade-off. Basing on a general equilibrium model by T. Kehoe including production and taxes we provide a formal model of an evolving economy fully accounting for the appearance of novelty. From this emerges in a natural way the notion of an open loop evolution equilibrium. It is based on arguments from the gradual vs. bang-bang tax reform controversy and from the debate on optimal macroeconomic policy design. Existence of equilibrium is established extending an analytical result which in a different context and independently has been proved by Mas- Colell and by the author. We use the term "kinetic" to indicate that in contrast to traditional comparative statics our approach neither hinges on the uniqueness of equilibria, nor is it confined to the analysis of prescribed parameter variations. --evolution,equilibrium,equilibrium price path,frictionless tuning of control parameters
On Bergman kernel functions and weak Morse inequalities
We give simple and unified proofs of weak holomorhpic Morse inequalities on
complete manifolds, -convex manifolds, pseudoconvex domains, weakly
-complete manifolds and covering manifolds. This paper is essentially based
on the asymptotic Bergman kernel functions and the Bochner-Kodaira-Nakano
formulas
Non-existence of multiple-black-hole solutions close to Kerr-Newman
We show that a stationary asymptotically flat electro-vacuum solution of
Einstein's equations that is everywhere locally "almost isometric" to a
Kerr-Newman solution cannot admit more than one event horizon. Axial symmetry
is not assumed. In particular this implies that the assumption of a single
event horizon in Alexakis-Ionescu-Klainerman's proof of perturbative uniqueness
of Kerr black holes is in fact unnecessary.Comment: Version 2: improved presentation; no changes to the result. Version
3: corrected an oversight in the historical review. Version 4: version
accepted for publicatio
Adaptive filtering techniques for gravitational wave interferometric data: Removing long-term sinusoidal disturbances and oscillatory transients
It is known by the experience gained from the gravitational wave detector
proto-types that the interferometric output signal will be corrupted by a
significant amount of non-Gaussian noise, large part of it being essentially
composed of long-term sinusoids with slowly varying envelope (such as violin
resonances in the suspensions, or main power harmonics) and short-term ringdown
noise (which may emanate from servo control systems, electronics in a
non-linear state, etc.). Since non-Gaussian noise components make the detection
and estimation of the gravitational wave signature more difficult, a denoising
algorithm based on adaptive filtering techniques (LMS methods) is proposed to
separate and extract them from the stationary and Gaussian background noise.
The strength of the method is that it does not require any precise model on the
observed data: the signals are distinguished on the basis of their
autocorrelation time. We believe that the robustness and simplicity of this
method make it useful for data preparation and for the understanding of the
first interferometric data. We present the detailed structure of the algorithm
and its application to both simulated data and real data from the LIGO 40meter
proto-type.Comment: 16 pages, 9 figures, submitted to Phys. Rev.
Riemannian geometry for efficient analysis of protein dynamics data
An increasingly common viewpoint is that protein dynamics data sets reside in
a non-linear subspace of low conformational energy. Ideal data analysis tools
for such data sets should therefore account for such non-linear geometry. The
Riemannian geometry setting can be suitable for a variety of reasons. First, it
comes with a rich structure to account for a wide range of geometries that can
be modelled after an energy landscape. Second, many standard data analysis
tools initially developed for data in Euclidean space can also be generalised
to data on a Riemannian manifold. In the context of protein dynamics, a
conceptual challenge comes from the lack of a suitable smooth manifold and the
lack of guidelines for constructing a smooth Riemannian structure based on an
energy landscape. In addition, computational feasibility in computing geodesics
and related mappings poses a major challenge. This work considers these
challenges. The first part of the paper develops a novel local approximation
technique for computing geodesics and related mappings on Riemannian manifolds
in a computationally feasible manner. The second part constructs a smooth
manifold of point clouds modulo rigid body group actions and a Riemannian
structure that is based on an energy landscape for protein conformations. The
resulting Riemannian geometry is tested on several data analysis tasks relevant
for protein dynamics data. It performs exceptionally well on coarse-grained
molecular dynamics simulated data. In particular, the geodesics with given
start- and end-points approximately recover corresponding molecular dynamics
trajectories for proteins that undergo relatively ordered transitions with
medium sized deformations. The Riemannian protein geometry also gives
physically realistic summary statistics and retrieves the underlying dimension
even for large-sized deformations within seconds on a laptop
Control of Nonholonomic Systems and Sub-Riemannian Geometry
Lectures given at the CIMPA School "Geometrie sous-riemannienne", Beirut,
Lebanon, 201
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