251 research outputs found
A Ky Fan minimax inequality for quasiequilibria on finite dimensional spaces
Several results concerning existence of solutions of a quasiequilibrium
problem defined on a finite dimensional space are established. The proof of the
first result is based on a Michael selection theorem for lower semicontinuous
set-valued maps which holds in finite dimensional spaces. Furthermore this
result allows one to locate the position of a solution. Sufficient conditions,
which are easier to verify, may be obtained by imposing restrictions either on
the domain or on the bifunction. These facts make it possible to yield various
existence results which reduce to the well known Ky Fan minimax inequality when
the constraint map is constant and the quasiequilibrium problem coincides with
an equilibrium problem. Lastly, a comparison with other results from the
literature is discussed
Relevance of phonon dynamics in strongly correlated systems coupled to phonons: A Dynamical Mean Field Theory analysis
The properties of the electron-phonon interaction in the presence of a
sizable electronic repulsion at finite doping are studied by investigating the
metallic phase of the Hubbard-Holstein model with Dynamical Mean Field Theory.
Analyzing the quasiparticle weight at finite doping, we find that a large
Coulomb repulsion reduces the effect of electron-phonon coupling at low-energy,
while this reduction is not present at high energy. The renormalization of the
electron-phonon coupling induced by the Hubbard repul sion depends in a
surprisingly strong and non-trivial way on the phonon frequency. Our results
suggest that phonon might affect differently high-energy and low-energy
properties and this, together with the effect of phonon dynamics, should be
carefully taken into account when the effects of the electron-phonon
interaction in a strongly correlated system, like the superconducting cuprates,
are discussed.Comment: 10 pages, 7 figures - revised version with minor change
Finite-density corrections to the Unitary Fermi gas: A lattice perspective from Dynamical Mean-Field Theory
We investigate the approach to the universal regime of the dilute unitary
Fermi gas as the density is reduced to zero in a lattice model. To this end we
study the chemical potential, superfluid order parameter and internal energy of
the attractive Hubbard model in three different lattices with densities of
states (DOS) which share the same low-energy behavior of fermions in
three-dimensional free space: a cubic lattice, a "Bethe lattice" with a
semicircular DOS, and a "lattice gas" with parabolic dispersion and a sharp
energy cut-off that ensures the normalization of the DOS. The model is solved
using Dynamical Mean-Field Theory, that treats directly the thermodynamic limit
and arbitrarily low densities, eliminating finite-size effects. At densities of
the order of one fermion per site the lattice and its specific form dominate
the results. The evolution to the low-density limit is smooth and it does not
allow to define an unambiguous low-density regime. Such finite-density effects
are significantly reduced using the lattice gas, and they are maximal for the
three-dimensional cubic lattice. Even though dynamical mean-field theory is
bound to reduce to the more standard static mean field in the limit of zero
density due to the local nature of the self-energy and of the vertex functions,
it compares well with accurate Monte Carlo simulations down to the lowest
densities accessible to the latter.Comment: 9 pages, 8 figure
An Optimality Approach to the Application Ratio for the Matching Adjustment in the Solvency II Regime
We refer to the Technical Specifications provided by EIOPA to implement
the package of long-term guarantees measures which shall be included into
the Solvency II Framework Directive. One of these regulatory measures concernes
the Application Ratio, a coefficient defining what portion of the Maximum Matching Adjustment
an insurance company can apply to the risk-free rates for discounting
her obligations, given the matching properties of the assigned asset portfolio.
In this paper we propose an optimization algorithm providing a reliable assessment of the Application Ratio.
The Application Ratio provided by the algorithm is optimal in the sense that it has the maximum value given the
structure %matching properties of the asset-liability portfolio. This value corresponds to the minimum attainable level for
the losses incurred from forced sales of defaultable bonds with mispriced market value.
We show that under natural assumptions this optimality problem has the form of a linear programming problem,
which can be easily solved using standard numerical procedures.
A matching criterion defined in stronger form can also be applied by imposing appropriate
run-off constraints in the linear programming problem.
The value of the optimal Application Ratio can be used by a Supervisor as an objective benchmark for checking the
appropriateness of the Application Ratio adopted by the undertaking.
The optimal liquidation policy provided by the algorithm can also be used by an insurance undertaking which want to apply
conservative management actions to her asset-liability portfolio
Strongly Correlated Superconductivity rising from a Pseudo-gap Metal
We solve by Dynamical Mean Field Theory a toy-model which has a phase diagram
strikingly similar to that of high superconductors: a bell-shaped
superconducting region adjacent the Mott insulator and a normal phase that
evolves from a conventional Fermi liquid to a pseudogapped semi-metal as the
Mott transition is approached. Guided by the physics of the impurity model that
is self-consistently solved within Dynamical Mean Field Theory, we introduce an
analytical ansatz to model the dynamical behavior across the various phases
which fits very accurately the numerical data. The ansatz is based on the
assumption that the wave-function renormalization, that is very severe
especially in the pseudogap phase close to the Mott transition, is perfectly
canceled by the vertex corrections in the Cooper pairing channel.A remarkable
outcome is that a superconducting state can develop even from a pseudogapped
normal state, in which there are no low-energy quasiparticles. The overall
physical scenario that emerges, although unraveled in a specific model and in
an infinite-coordination Bethe lattice, can be interpreted in terms of so
general arguments to suggest that it can be realized in other correlated
systems.Comment: 14 pages, 11 figure
Quantifying the relevance of different mediators in the human immune cell network
Immune cells coordinate their efforts for the correct and efficient
functioning of the immune system (IS). Each cell type plays a distinct role and
communicates with other cell types through mediators such as cytokines,
chemokines and hormones, among others, that are crucial for the functioning of
the IS and its fine tuning. Nevertheless, a quantitative analysis of the
topological properties of an immunological network involving this complex
interchange of mediators among immune cells is still lacking. Here we present a
method for quantifying the relevance of different mediators in the immune
network, which exploits a definition of centrality based on the concept of
efficient communication. The analysis, applied to the human immune system,
indicates that its mediators significantly differ in their network relevance.
We found that cytokines involved in innate immunity and inflammation and some
hormones rank highest in the network, revealing that the most prominent
mediators of the IS are molecules involved in these ancestral types of defence
mechanisms highly integrated with the adaptive immune response, and at the
interplay among the nervous, the endocrine and the immune systems.Comment: 10 pages, 3 figure
Local cone approximations in mathematical programming
We show how to use intensively local cone approximations to obtain results in some fields of optimization theory as optimality conditions, constraint qualifications, mean value theorems and error bound
Existence and solution methods for equilibria
Equilibrium problems provide a mathematical framework which includes optimization, variational inequalities, fixed-point and saddle point problems, and noncooperative games as particular cases. This general format received an increasing interest in the last decade mainly because many theoretical and algorithmic results developed for one of these models can be often extended to the others through the unifying language provided by this common format. This survey paper aims at covering the main results concerning the existence of equilibria and the solution methods for finding them
X-Ray Resonant Scattering as a Direct Probe of Orbital Ordering in Transition-Metal Oxides
X-ray resonant scattering at the K-edge of transition metal oxides is shown
to measure the orbital order parameter, supposed to accompany magnetic ordering
in some cases. Virtual transitions to the 3d-orbitals are quadrupolar in
general. In cases with no inversion symmetry, such as VO, treated in
detail here, a dipole component enhances the resonance. Hence, we argue that
the detailed structure of orbital order in VO is experimentally
accessible.Comment: LaTex using RevTex, 4 pages and two included postscript figure
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