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

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

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

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