7,284 research outputs found
A hydrodynamical homotopy co-momentum map and a multisymplectic interpretation of higher order linking numbers
In this article a homotopy co-momentum map (\`a la
Callies-Fr\'egier-Rogers-Zambon) trangressing to the standard hydrodynamical
co-momentum map of Arnol'd, Marsden and Weinstein and others is constructed and
then generalized to a special class of Riemannian manifolds. Also, a covariant
phase space interpretation of the coadjoint orbits associated to the Euler
evolution for perfect fluids and in particular of Brylinski's manifold of
smooth oriented knots is discussed. As an application of the above homotopy
co-momentum map, a reinterpretation of the (Massey) higher order linking
numbers in terms of conserved quantities within the multisymplectic framework
is provided and knot theoretic analogues of first integrals in involution are
determined.Comment: 21 pages, 3 figures. The present version focuses on the connections
between multisymplectic geometry, hydrodynamics and vortices. The derivation
of the HOMFLYPT polynomial via geometric quantization has been proposed as a
separate preprint, see "Derivation of the HOMFLYPT knot polynomial via
helicity and geometric quantization ", arXiv:1910.xxx
Informational power of quantum measurements
We introduce the informational power of a quantum measurement as the maximum
amount of classical information that the measurement can extract from any
ensemble of quantum states. We prove the additivity by showing that the
informational power corresponds to the classical capacity of a
quantum-classical channel. We restate the problem of evaluating the
informational power as the maximization of the accessible information of a
suitable ensemble. We provide a numerical algorithm to find an optimal
ensemble, and quantify the informational power.Comment: 9 pages, 3 figures, added references, published versio
A Game-Theoretic Approach for Runtime Capacity Allocation in MapReduce
Nowadays many companies have available large amounts of raw, unstructured
data. Among Big Data enabling technologies, a central place is held by the
MapReduce framework and, in particular, by its open source implementation,
Apache Hadoop. For cost effectiveness considerations, a common approach entails
sharing server clusters among multiple users. The underlying infrastructure
should provide every user with a fair share of computational resources,
ensuring that Service Level Agreements (SLAs) are met and avoiding wastes. In
this paper we consider two mathematical programming problems that model the
optimal allocation of computational resources in a Hadoop 2.x cluster with the
aim to develop new capacity allocation techniques that guarantee better
performance in shared data centers. Our goal is to get a substantial reduction
of power consumption while respecting the deadlines stated in the SLAs and
avoiding penalties associated with job rejections. The core of this approach is
a distributed algorithm for runtime capacity allocation, based on Game Theory
models and techniques, that mimics the MapReduce dynamics by means of
interacting players, namely the central Resource Manager and Class Managers
How much a Quantum Measurement is Informative?
The informational power of a quantum measurement is the maximum amount of
classical information that the measurement can extract from any ensemble of
quantum states. We discuss its main properties. Informational power is an
additive quantity, being equivalent to the classical capacity of a
quantum-classical channel. The informational power of a quantum measurement is
the maximum of the accessible information of a quantum ensemble that depends on
the measurement. We present some examples where the symmetry of the measurement
allows to analytically derive its informational power.Comment: 3 pages, 2 figures, published in the proceedings of the 11th Quantum
Communication, Measurement, and Computing (QCMC) conference, Vienna, Austria,
30 July-3 August, 201
Cosmic Star Formation: a simple model of the SFRD(z)
We investigate the evolution of the cosmic star formation rate density (SFRD)
from redshift z=20 to z=0 and compare it with the observational one by Madau
and Dickinson derived from recent compilations of UV and IR data. The
theoretical SFRD(z) and its evolution are obtained using a simple model which
folds together the star formation histories of prototype galaxies designed to
represent real objects of different morphological type along the Hubble
sequence and the hierarchical growing of structures under the action of gravity
from small perturbations to large scale objects in \Lambda-CDM cosmogony, i.e.
the number density of dark matter halos N(M,z). Although the overall model is
very simple and easy to set up, it provides results that well mimic those
obtained from large scale N-body simulations of great complexity. The
simplicity of our approach allows us to test different assumptions for the star
formation law in galaxies, the effects of energy feedback from stars to
interstellar gas and the efficiency of galactic winds, and also the effect of
N(M,z). The result of our analysis is that in the framework of the hierarchical
assembly of galaxies the so-called time-delayed star formation under plain
assumptions mainly for the energy feedback and galactic winds can reproduce the
observational SFRD(z).Comment: ApJ (accepted for publication
Work statistics, irreversible heat and correlations build-up in joining two spin chains
We investigate the influences of quantum many-body effects, such as
criticality and the existence of factorisation fields, in the thermodynamic
cost of establishing a bonding link between two independent quantum spin
chains. We provide a physical interpretation of the behavior of irreversible
work spent in such process by linking the phenomenology of such quantities to
the properties of the spectrum of the systemComment: 9 pages, 8 figures. Contribution to the FQMT13 special volum
Mean Field Games Incorporating Carryover Effects: Optimizing Advertising Models
We consider a class of optimal control problems that arise in connection with
optimal advertising under uncertainty. Two main features appear in the model: a
delay in the control variable driving the state dynamics; a mean-field term
both in the state dynamics and in the utility functional, taking into account
for other agents. We interpret the model in a competitive environment, hence we
set it in the framework of Mean Field Games. We rephrase the problem in an
infinite dimensional setting, in order to obtain the associated Mean Field Game
system. Finally, we specify the problem to a simple case, and solve it
providing an explicit solution.Comment: 13 page
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