7,132 research outputs found
Fixation in Evolutionary Games under Non-Vanishing Selection
One of the most striking effect of fluctuations in evolutionary game theory
is the possibility for mutants to fixate (take over) an entire population.
Here, we generalize a recent WKB-based theory to study fixation in evolutionary
games under non-vanishing selection, and investigate the relation between
selection intensity w and demographic (random) fluctuations. This allows the
accurate treatment of large fluctuations and yields the probability and mean
times of fixation beyond the weak selection limit. The power of the theory is
demonstrated on prototypical models of cooperation dilemmas with multiple
absorbing states. Our predictions compare excellently with numerical
simulations and, for finite w, significantly improve over those of the
Fokker-Planck approximation.Comment: 4 figures, to appear in EPL (Europhysics Letters
Learning from power system data stream: phasor-detective approach
Assuming access to synchronized stream of Phasor Measurement Unit (PMU) data
over a significant portion of a power system interconnect, say controlled by an
Independent System Operator (ISO), what can you extract about past, current and
future state of the system? We have focused on answering this practical
questions pragmatically - empowered with nothing but standard tools of data
analysis, such as PCA, filtering and cross-correlation analysis. Quite
surprisingly we have found that even during the quiet "no significant events"
period this standard set of statistical tools allows the "phasor-detective" to
extract from the data important hidden anomalies, such as problematic control
loops at loads and wind farms, and mildly malfunctioning assets, such as
transformers and generators. We also discuss and sketch future challenges a
mature phasor-detective can possibly tackle by adding machine learning and
physics modeling sophistication to the basic approach
Prescriptions on antiproton cross section data for precise theoretical antiproton flux predictions
After the breakthrough from the satellite-borne PAMELA detector, the flux of
cosmic-ray (CR) antiprotons has been provided with unprecedented accuracy by
AMS-02 on the International Space Station. Its data spans an energy range from
below 1 GeV up to 400 GeV and most of the data points contain errors below the
amazing level of 5%. The bulk of the antiproton flux is expected to be produced
by the scatterings of CR protons and helium off interstellar hydrogen and
helium atoms at rest. The modeling of these interactions, which requires the
relevant production cross sections, induces an uncertainty in the determination
of the antiproton source term that can even exceed the uncertainties in the CR
data itself. The aim of the present analysis is to determine the
uncertainty required for cross section
measurements such that the induced uncertainties on the flux are at
the same level. Our results are discussed both in the center-of-mass reference
frame, suitable for collider experiments, and in the laboratory frame, as
occurring in the Galaxy. We find that cross section data should be collected
with accuracy better that few percent with proton beams from 10 GeV to 6 TeV
and a pseudorapidity ranging from 2 to almost 8 or, alternatively, with
from 0.04 to 2 GeV and from 0.02 to 0.7. Similar considerations
hold for the He production channel. The present collection of data is far
from these requirements. Nevertheless, they could, in principle, be reached by
fixed target experiments with beam energies in the reach of CERN accelerators.Comment: 15 pages, 13 figures, matches published versio
Production cross sections of cosmic antiprotons in the light of new data from the NA61 and LHCb experiments
The cosmic-ray flux of antiprotons is measured with high precision by the
space-borne particle spectrometers AMS-02.Its interpretation requires a correct
description of the dominant production process for antiprotons in our Galaxy,
namely, the interaction of cosmic-ray proton and helium with the interstellar
medium. In the light of new cross section measurements by the NA61 experiment
of and the first ever measurement of by the LHCb experiment, we update the
parametrization of proton-proton and proton-nucleon cross sections.We find that
the LHCb He data constrain a shape for the cross section at high energies
and show for the first time how well the rescaling from the channel
applies to a helium target. By using , He and C data we estimate the
uncertainty on the Lorentz invariant cross section for . We use these new cross sections to compute the source
term for all the production channels, considering also nuclei heavier than He
both in cosmic rays and the interstellar medium. The uncertainties on the total
source term are at the level of % and slightly increase below antiproton
energies of 5 GeV. This uncertainty is dominated by the cross section, which translates into all channels since we derive
them using the cross sections. The cross sections to calculate the source
spectra from all relevant cosmic-ray isotopes are provided in the Supplemental
Material. We finally quantify the necessity of new data on antiproton
production cross sections, and pin down the kinematic parameter space which
should be covered by future data.Comment: 16 pages, 11 figures, matches published 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
Projections from Subvarieties
Let be an n-dimensional connected projective submanifold of
projective space. Let denote the projection from a
linear . Assuming that we have the induced
rational mapping . This article started as an
attempt to understand the structure of this mapping when has a lower
dimensional image. In this case of necessity we have is
nonempty. We have in this article studied a closely related question, which
includes many special cases including the case when the center of the
projection \pn q is contained in .
PROBLEM. Let be a proper connected k-dimensional projective submanifold
of an -dimensional projective manifold . Assume that . Let be a
very ample line bundle on such that is spanned by global
sections, where denotes the ideal sheaf of in . Describe the
structure of under the additional assumption that the image of
under the mapping associated to is lower dimensional
efficiency and evolution of R&D Networks.
This work introduces a new model to investigate the efficiency and evolution of networks of firms exchanging knowledge in R&D partnerships. We first examine the efficiency of a given network structure from the point of view of maximizing total profits in the industry. We show that the efficient network structure depends on the marginal cost of collaboration. When the marginal cost is low, the complete graph is efficient. However, a high marginal cost implies that the efficient network is sparser and has a core-periphery structure. Next, we examine the evolution of the network structure when the decision on collaborating partners is decentralized. We show the existence of multiple equilibrium structures which are in general inefficient. This is due to (i) the path dependent character of the partner selection process, (ii) the presence of knowledge externalities and (iii) the presence of severance costs involved in link deletion. Finally, we study the properties of the emerging equilibrium networks and we show that they are coherent with the stylized facts on R&D networks.R&D networks;technology spillovers;network efficiency;network formation;
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