215 research outputs found
Policy Gradients for CVaR-Constrained MDPs
We study a risk-constrained version of the stochastic shortest path (SSP)
problem, where the risk measure considered is Conditional Value-at-Risk (CVaR).
We propose two algorithms that obtain a locally risk-optimal policy by
employing four tools: stochastic approximation, mini batches, policy gradients
and importance sampling. Both the algorithms incorporate a CVaR estimation
procedure, along the lines of Bardou et al. [2009], which in turn is based on
Rockafellar-Uryasev's representation for CVaR and utilize the likelihood ratio
principle for estimating the gradient of the sum of one cost function
(objective of the SSP) and the gradient of the CVaR of the sum of another cost
function (in the constraint of SSP). The algorithms differ in the manner in
which they approximate the CVaR estimates/necessary gradients - the first
algorithm uses stochastic approximation, while the second employ mini-batches
in the spirit of Monte Carlo methods. We establish asymptotic convergence of
both the algorithms. Further, since estimating CVaR is related to rare-event
simulation, we incorporate an importance sampling based variance reduction
scheme into our proposed algorithms
Non-equilibrium transition from dissipative quantum walk to classical random walk
We have investigated the time-evolution of a free particle in interaction
with a phonon thermal bath, using the tight-binding approach. A dissipative
quantum walk can be defined and many important non-equilibrium decoherence
properties can be investigated analytically. The non-equilibrium statistics of
a pure initial state have been studied. Our theoretical results indicate that
the evolving wave-packet shows the suppression of Anderson's boundaries
(ballistic peaks) by the presence of dissipation. Many important relaxation
properties can be studied quantitatively, such as von Neumann's entropy and
quantum purity. In addition, we have studied Wigner's function. The
time-dependent behavior of the quantum entanglement between a free particle -in
the lattice- and the phonon bath has been characterized analytically. This
result strongly suggests the non-trivial time-dependence of the off-diagonal
elements of the reduced density matrix of the system. We have established a
connection between the quantum decoherence and the dissipative parameter
arising from interaction with the phonon bath. The time-dependent behavior of
quantum correlations has also been pointed out, showing continuous transition
from quantum random walk to classical random walk, when dissipation increases.Comment: Submitted for publication. 17 pages, 6 figure
Exact and explicit probability densities for one-sided Levy stable distributions
We study functions g_{\alpha}(x) which are one-sided, heavy-tailed Levy
stable probability distributions of index \alpha, 0< \alpha <1, of fundamental
importance in random systems, for anomalous diffusion and fractional kinetics.
We furnish exact and explicit expression for g_{\alpha}(x), 0 \leq x < \infty,
satisfying \int_{0}^{\infty} exp(-p x) g_{\alpha}(x) dx = exp(-p^{\alpha}),
p>0, for all \alpha = l/k < 1, with k and l positive integers. We reproduce all
the known results given by k\leq 4 and present many new exact solutions for k >
4, all expressed in terms of known functions. This will allow a 'fine-tuning'
of \alpha in order to adapt g_{\alpha}(x) to a given experimental situation.Comment: 4 pages, 3 figures and 1 tabl
Magnetically Torqued Thin Accretion Disks
We compute the properties of a geometrically thin, steady accretion disk
surrounding a central rotating, magnetized star. The magnetosphere is assumed
to entrain the disk over a wide range of radii. The model is simplified in that
we adopt two (alternate) ad hoc, but plausible, expressions for the azimuthal
component of the magnetic field as a function of radial distance. We find a
solution for the angular velocity profile tending to corotation close to the
central star, and smoothly matching a Keplerian curve at a radius where the
viscous stress vanishes. The value of this ''transition'' radius is nearly the
same for both of our adopted B-field models. We then solve analytically for the
torques on the central star and for the disk luminosity due to gravity and
magnetic torques. When expressed in a dimensionless form, the resulting
quantities depend on one parameter alone, the ratio of the transition radius to
the corotation radius. For rapid rotators, the accretion disk may be powered
mostly by spin-down of the central star. These results are independent of the
viscosity prescription in the disk. We also solve for the disk structure for
the special case of an optically thick alpha disk. Our results are applicable
to a range of astrophysical systems including accreting neutron stars,
intermediate polar cataclysmic variables, and T Tauri systems.Comment: 9 sharper figs, updated reference
Dicke-Type Energy Level Crossings in Cavity-Induced Atom Cooling: Another Superradiant Cooling
This paper is devoted to energy-spectral analysis for the system of a
two-level atom coupled with photons in a cavity. It is shown that the
Dicke-type energy level crossings take place when the atom-cavity interaction
of the system undergoes changes between the weak coupling regime and the strong
one. Using the phenomenon of the crossings we develop the idea of
cavity-induced atom cooling proposed by the group of Ritsch, and we lay
mathematical foundations of a possible mechanism for another superradiant
cooling in addition to that proposed by Domokos and Ritsch. The process of our
superradiant cooling can function well by cavity decay and by control of the
position of the atom, at least in (mathematical) theory, even if there is
neither atomic absorption nor atomic emission of photons.Comment: 15 pages; 8 figure
Nonlinear equation for anomalous diffusion: unified power-law and stretched exponential exact solution
The nonlinear diffusion equation is analyzed here, where , and , and are real parameters.
This equation unifies the anomalous diffusion equation on fractals ()
and the spherical anomalous diffusion for porous media (). Exact
point-source solution is obtained, enabling us to describe a large class of
subdiffusion (), normal diffusion () and
superdiffusion (). Furthermore, a thermostatistical basis
for this solution is given from the maximum entropic principle applied to the
Tsallis entropy.Comment: 3 pages, 2 eps figure
Integrated random processes exhibiting long tails, finite moments and 1/f spectra
A dynamical model based on a continuous addition of colored shot noises is
presented. The resulting process is colored and non-Gaussian. A general
expression for the characteristic function of the process is obtained, which,
after a scaling assumption, takes on a form that is the basis of the results
derived in the rest of the paper. One of these is an expansion for the
cumulants, which are all finite, subject to mild conditions on the functions
defining the process. This is in contrast with the Levy distribution -which can
be obtained from our model in certain limits- which has no finite moments. The
evaluation of the power spectrum and the form of the probability density
function in the tails of the distribution shows that the model exhibits a 1/f
spectrum and long tails in a natural way. A careful analysis of the
characteristic function shows that it may be separated into a part representing
a Levy processes together with another part representing the deviation of our
model from the Levy process. This allows our process to be viewed as a
generalization of the Levy process which has finite moments.Comment: Revtex (aps), 15 pages, no figures. Submitted to Phys. Rev.
Gravitating discs around black holes
Fluid discs and tori around black holes are discussed within different
approaches and with the emphasis on the role of disc gravity. First reviewed
are the prospects of investigating the gravitational field of a black
hole--disc system by analytical solutions of stationary, axially symmetric
Einstein's equations. Then, more detailed considerations are focused to middle
and outer parts of extended disc-like configurations where relativistic effects
are small and the Newtonian description is adequate.
Within general relativity, only a static case has been analysed in detail.
Results are often very inspiring, however, simplifying assumptions must be
imposed: ad hoc profiles of the disc density are commonly assumed and the
effects of frame-dragging and completely lacking. Astrophysical discs (e.g.
accretion discs in active galactic nuclei) typically extend far beyond the
relativistic domain and are fairly diluted. However, self-gravity is still
essential for their structure and evolution, as well as for their radiation
emission and the impact on the environment around. For example, a nuclear star
cluster in a galactic centre may bear various imprints of mutual star--disc
interactions, which can be recognised in observational properties, such as the
relation between the central mass and stellar velocity dispersion.Comment: Accepted for publication in CQG; high-resolution figures will be
available from http://www.iop.org/EJ/journal/CQ
Track reconstruction and matching between emulsion and silicon pixel detectors for the SHiP-charm experiment
In July 2018 an optimization run for the proposed charm cross section measurement for SHiP was performed at the CERN SPS. A heavy, moving target instrumented with nuclear emulsion films followed by a silicon pixel tracker was installed in front of the Goliath magnet at the H4 proton beam-line. Behind the magnet, scintillating-fibre, drift-tube and RPC detectors were placed. The purpose of this run was to validate the measurement's feasibility, to develop the required analysis tools and fine-tune the detector layout. In this paper, we present the track reconstruction in the pixel tracker and the track matching with the moving emulsion detector. The pixel detector performed as expected and it is shown that, after proper alignment, a vertex matching rate of 87% is achieved
Rapidly Changing Range Limits in a Warming World: Critical Data Limitations and Knowledge Gaps for Advancing Understanding of Mangrove Range Dynamics in the Southeastern USA
Climate change is altering species’ range limits and transforming ecosystems. For example, warming temperatures are leading to the range expansion of tropical, cold-sensitive species at the expense of their cold-tolerant counterparts. In some temperate and subtropical coastal wetlands, warming winters are enabling mangrove forest encroachment into salt marsh, which is a major regime shift that has significant ecological and societal ramifications. Here, we synthesized existing data and expert knowledge to assess the distribution of mangroves near rapidly changing range limits in the southeastern USA. We used expert elicitation to identify data limitations and highlight knowledge gaps for advancing understanding of past, current, and future range dynamics. Mangroves near poleward range limits are often shorter, wider, and more shrublike compared to their tropical counterparts that grow as tall forests in freeze-free, resource-rich environments. The northern range limits of mangroves in the southeastern USA are particularly dynamic and climate sensitive due to abundance of suitable coastal wetland habitat and the exposure of mangroves to winter temperature extremes that are much colder than comparable range limits on other continents. Thus, there is need for methodological refinements and improved spatiotemporal data regarding changes in mangrove structure and abundance near northern range limits in the southeastern USA. Advancing understanding of rapidly changing range limits is critical for foundation plant species such as mangroves, as it provides a basis for anticipating and preparing for the cascading effects of climate-induced species redistribution on ecosystems and the human communities that depend on their ecosystem services
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