311 research outputs found
Bounded Representations of Interval and Proper Interval Graphs
Klavik et al. [arXiv:1207.6960] recently introduced a generalization of
recognition called the bounded representation problem which we study for the
classes of interval and proper interval graphs. The input gives a graph G and
in addition for each vertex v two intervals L_v and R_v called bounds. We ask
whether there exists a bounded representation in which each interval I_v has
its left endpoint in L_v and its right endpoint in R_v. We show that the
problem can be solved in linear time for interval graphs and in quadratic time
for proper interval graphs.
Robert's Theorem states that the classes of proper interval graphs and unit
interval graphs are equal. Surprisingly the bounded representation problem is
polynomially solvable for proper interval graphs and NP-complete for unit
interval graphs [Klav\'{\i}k et al., arxiv:1207.6960]. So unless P = NP, the
proper and unit interval representations behave very differently.
The bounded representation problem belongs to a wider class of restricted
representation problems. These problems are generalizations of the
well-understood recognition problem, and they ask whether there exists a
representation of G satisfying some additional constraints. The bounded
representation problems generalize many of these problems
(Semi-)Predictive Discretization During Model Selection
In this paper, we present an approach to discretizing multivariate continuous data while learning the structure of a graphical model. We derive the joint scoring function from the principle of predictive accuracy, which inherently ensures the optimal trade-off between goodness of fit and model complexity (including the number of discretization levels). Using the so-called finest grid implied by the data, our scoring function depends only on the number of data points in the various discretization levels. Not only can it be computed efficiently, but it is also independent of the metric used in the continuous space. Our experiments with gene expression data show that discretization plays a crucial role regarding the resulting network structure
Coherence as ultrashort pulse train generator
Intense, well-controlled regular light pulse trains start to play a crucial
role in many fields of physics. We theoretically demonstrate a very simple and
robust technique for generating such periodic ultrashort pulses from a
continuous probe wave which propagates in a dispersive thermal gas media
Reconciling observed GRB prompt spectra with synchrotron radiation ?
(abridged)Prompt GRB emission is often interpreted as synchrotron radiation
from high-energy electrons accelerated in internal shocks. Fast synchrotron
cooling predicts that the photon index below the spectral peak is alpha=-3/2.
This differs significantly from the observed median value alpha \approx -1. We
quantify the influence of inverse Compton and adiabatic cooling on alpha to
understand whether these processes can reconcile the observations with a
synchrotron origin. We use a time-dependent code that follows both the shock
dynamics and electron energy losses. We investigate the dependence of alpha on
the parameters of the model. Slopes between -3/2 and -1 are reached when
electrons suffer IC losses in the Klein-Nishina regime. This does not
necessarily imply a strong IC component in the Fermi/LAT range because
scatterings are only moderately efficient. Steep slopes require that a large
fraction (10-30%) of the dissipated energy is given to a small fraction (<~1%)
of the electrons and that the magnetic energy density fraction remains low (<~
0.1%). Values of alpha up to -2/3 can be obtained with relatively high
radiative efficiencies (>50%) when adiabatic cooling is comparable with
radiative cooling (marginally fast cooling). This requires collisions at small
radii and/or with low magnetic fields. Amending the standard fast cooling
scenario to account for IC cooling naturally leads to alpha up to -1.
Marginally fast cooling may also account for alpha up to -2/3, although the
conditions required are more difficult to reach. About 20% of GRBs show spectra
with slopes alpha>-2/3. Other effects, not investigated here, such as a thermal
component in the electron distribution or pair production by HE photons may
further affect alpha. Still, the majority of observed GRB prompt spectra can be
reconciled with a synchrotron origin, constraining the microphysics of mildly
relativistic internal shocks.Comment: 14 pages, 10 figures, accepted for publication in A&A (10/10/2010
Using Gamma-Ray Burst Prompt Emission to Probe Relativistic Shock Acceleration
It is widely accepted that the prompt transient signal in the 10 keV - 10 GeV
band from gamma-ray bursts (GRBs) arises from multiple shocks internal to the
ultra-relativistic expansion. The detailed understanding of the dissipation and
accompanying acceleration at these shocks is a currently topical subject. This
paper explores the relationship between GRB prompt emission spectra and the
electron (or ion) acceleration properties at the relativistic shocks that
pertain to GRB models. The focus is on the array of possible high-energy
power-law indices in accelerated populations, highlighting how spectra above 1
MeV can probe the field obliquity in GRB internal shocks, and the character of
hydromagnetic turbulence in their environs. It is emphasized that diffusive
shock acceleration theory generates no canonical spectrum at relativistic MHD
discontinuities. This diversity is commensurate with the significant range of
spectral indices discerned in prompt burst emission. Such system diagnostics
are now being enhanced by the broadband spectral coverage of bursts by the
Fermi Gamma-Ray Space Telescope; while the Gamma-Ray Burst Monitor (GBM)
provides key diagnostics on the lower energy portions of the particle
population, the focus here is on constraints in the non-thermal, power-law
regime of the particle distribution that are provided by the Large Area
Telescope (LAT).Comment: 15 pages, 2 figures. Accepted for publication in Advances of Space
Researc
A Mathematical Framework for Agent Based Models of Complex Biological Networks
Agent-based modeling and simulation is a useful method to study biological
phenomena in a wide range of fields, from molecular biology to ecology. Since
there is currently no agreed-upon standard way to specify such models it is not
always easy to use published models. Also, since model descriptions are not
usually given in mathematical terms, it is difficult to bring mathematical
analysis tools to bear, so that models are typically studied through
simulation. In order to address this issue, Grimm et al. proposed a protocol
for model specification, the so-called ODD protocol, which provides a standard
way to describe models. This paper proposes an addition to the ODD protocol
which allows the description of an agent-based model as a dynamical system,
which provides access to computational and theoretical tools for its analysis.
The mathematical framework is that of algebraic models, that is, time-discrete
dynamical systems with algebraic structure. It is shown by way of several
examples how this mathematical specification can help with model analysis.Comment: To appear in Bulletin of Mathematical Biolog
Ultracold dense gas of deeply bound heteronuclear molecules
Recently, the quest for an ultracold and dense ensemble of polar molecules
has attracted strong interest. Polar molecules have bright prospects for novel
quantum gases with long-range and anisotropic interactions, for quantum
information science, and for precision measurements. However, high-density
clouds of ultracold polar molecules have so far not been produced. Here, we
report a key step towards this goal. Starting from an ultracold dense gas of
heteronuclear 40K-87Rb Feshbach molecules with typical binding energies of a
few hundred kHz and a negligible dipole moment, we coherently transfer these
molecules into a vibrational level of the ground-state molecular potential
bound by >10 GHz. We thereby increase the binding energy and the expected
dipole moment of the 40K-87Rb molecules by more than four orders of magnitude
in a single transfer step. Starting with a single initial state prepared with
Feshbach association, we achieve a transfer efficiency of 84%. While dipolar
effects are not yet observable, the presented technique can be extended to
access much more deeply bound vibrational levels and ultimately those
exhibiting a significant dipole moment. The preparation of an ultracold quantum
gas of polar molecules might therefore come within experimental reach.Comment: 5 pages, 5 figure
Impacts of selected Ecological Focus Area options in European farmed landscapes on climate regulation and pollination services: a systematic map protocol
Background: This systematic map protocol responds to an urgent policy need to evaluate key environmental benefits of new compulsory greening measures in the European Unionâs Common Agricultural Policy (CAP), with the aim of building a policy better linked to environmental performance. The systematic map will focus on Ecological Focus Areas (EFAs), in which larger arable farmers must dedicate 5% of their arable land to ecologically beneficial habitats, landscape features and land uses. The European Commissionâs Joint Research Centre has used a software tool called the âEFA calculatorâ to inform the European Commission about environmental benefits of EFA implementation. However, there are gaps in the EFA calculatorâs coverage of ecosystem services, especially âglobal climate regulationâ, and an opportunity to use systematic mapping methods to enhance its capture of evidence, in advance of forthcoming CAP reforms. We describe a method for assembling a database of relevant, peer-reviewed research conducted in all agricultural landscapes in Europe and neighbouring countries with similar biogeography, addressing the primary question: what are the impacts of selected EFA features in agricultural land on two policy-relevant ecosystem service outcomesâglobal climate regulation and pollination? The method is streamlined to allow results in good time for the current, time-limited opportunity to influence reforms of the CAP greening measures at European and Member State level. Methods: We will search four bibliographic databases in English, using a predefined and tested search string that focuses on a subset of EFA options and ecosystem service outcomes. The options and outcomes are selected as those with particular policy relevance and traction. Only articles in English will be included. We will screen search results at title, abstract and full text levels, recording the number of studies deemed non-relevant (with reasons at full text). A systematic map database that displays the meta-data (i.e. descriptive summary information about settings and methods) of relevant studies will be produced following full text assessment. The systematic map database will be published as a MS-Excel database. The nature and extent of the evidence base will be discussed, and the applicability of methods to convert the available evidence into EFA calculator scores will be assessed
Modeling the high-energy emission in GRB 110721A and implications on the early multiwavelength and polarimetric observations
GRB 110721A was detected by the Gamma-ray Burst Monitor and the Large Area
Telescope (LAT) onboard the Fermi satellite and the Gamma-ray Burst Polarimeter
onboard the IKAROS solar mission. Previous analysis done of this burst showed:
i) a linear polarization signal with position angle stable () and high degree of , ii) an extreme peak
energy of a record-breaking at 152 MeV, and iii) a subdominant prompt
thermal component observed right after the onset of this burst. In this paper,
the LAT data around the reported position of GRB 110721A are analysed with the
most recent software and then, the LAT light curve above 100 MeV was obtained.
The LAT light curve is modelled in terms of adiabatic early-afterglow external
shocks when the outflow propagates into a stellar wind. Additionally, we
discuss the possible origins and also study the implications of the
early-afterglow external shocks on the extreme peak energy observed at 152
MeV, the polarization observations and the subdominant prompt thermal
component.Comment: 9 pages and one figure. Accepted for publication in Ap
Modeling the Emission Processes in Blazars
Blazars are the most violent steady/recurrent sources of high-energy
gamma-ray emission in the known Universe. They are prominent emitters of
electromagnetic radiation throughout the entire electromagnetic spectrum. The
observable radiation most likely originates in a relativistic jet oriented at a
small angle with respect to the line of sight. This review starts out with a
general overview of the phenomenology of blazars, including results from a
recent multiwavelength observing campaign on 3C279. Subsequently, issues of
modeling broadband spectra will be discussed. Spectral information alone is not
sufficient to distinguish between competing models and to constrain essential
parameters, in particular related to the primary particle acceleration and
radiation mechanisms in the jet. Short-term spectral variability information
may help to break such model degeneracies, which will require snap-shot
spectral information on intraday time scales, which may soon be achievable for
many blazars even in the gamma-ray regime with the upcoming GLAST mission and
current advances in Atmospheric Cherenkov Telescope technology. In addition to
pure leptonic and hadronic models of gamma-ray emission from blazars,
leptonic/hadronic hybrid models are reviewed, and the recently developed
hadronic synchrotron mirror model for TeV gamma-ray flares which are not
accompanied by simultaneous X-ray flares (``orphan TeV flares'') is revisited.Comment: Invited Review at "The Multimessenger Approach to Gamma-Ray Sources",
Barcelona, Spain, July 2006; submitted to Astrophysics and Space Science. 10
pages, including 6 eps figures. Uses Springer's ApSS macro
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