Transfer from Multiple MDPs

Transfer reinforcement learning (RL) methods leverage on the experience collected on a set of source tasks to speed-up RL algorithms. A simple and effective approach is to transfer samples from source tasks and include them into the training set used to solve a given target task. In this paper, we investigate the theoretical properties of this transfer method and we introduce novel algorithms adapting the transfer process on the basis of the similarity between source and target tasks. Finally, we report illustrative experimental results in a continuous chain problem.Comment: 201

Higher homotopy of groups definable in o-minimal structures

It is known that a definably compact group G is an extension of a compact Lie group L by a divisible torsion-free normal subgroup. We show that the o-minimal higher homotopy groups of G are isomorphic to the corresponding higher homotopy groups of L. As a consequence, we obtain that all abelian definably compact groups of a given dimension are definably homotopy equivalent, and that their universal cover are contractible.Comment: 13 pages, to be published in the Israel Journal of Mathematic

Contact variational integrators

We present geometric numerical integrators for contact flows that stem from a discretization of Herglotz' variational principle. First we show that the resulting discrete map is a contact transformation and that any contact map can be derived from a variational principle. Then we discuss the backward error analysis of our variational integrators, including the construction of a modified Lagrangian. Throughout the paper we use the damped harmonic oscillator as a benchmark example to compare our integrators to their symplectic analogues

Lattice gauge theory model for graphene

The effects of the electromagnetic (e.m.) electron-electron interactions in half-filled graphene are investigated in terms of a lattice gauge theory model. By using exact Renormalization Group methods and lattice Ward Identities, we show that the e.m. interactions amplify the responses to the excitonic pairings associated to a Kekul\'e distortion and to a charge density wave. The effect of the electronic repulsion on the Peierls-Kekul\'e instability, usually neglected, is evaluated by deriving an exact non-BCS gap equation, from which we find evidence that strong e.m. interactions among electrons facilitate the spontaneous distortion of the lattice and the opening of a gap.Comment: 5 pages, 2 figures; typos corrected. Final version published in Phys. Rev.

Discrete subgroups of locally definable groups

We work in the category of locally definable groups in an o-minimal expansion of a field. Eleftheriou and Peterzil conjectured that every definably generated abelian connected group G in this category is a cover of a definable group. We prove that this is the case under a natural convexity assumption inspired by the same authors, which in fact gives a necessary and sufficient condition. The proof is based on the study of the zero-dimensional compatible subgroups of G. Given a locally definable connected group G (not necessarily definably generated), we prove that the n-torsion subgroup of G is finite and that every zero-dimensional compatible subgroup of G has finite rank. Under a convexity hypothesis we show that every zero-dimensional compatible subgroup of G is finitely generated.Comment: Final version. 17 pages. To appear in Selecta Mathematic

Absence of interaction corrections in graphene conductivity

The exact vanishing of the interaction corrections to the zero temperature and zero frequency conductivity of graphene in the presence of weak short range interactions is rigorously established.Comment: 4 page

CLUSTERING THE HETEROGENITY OF EU URBAN PERFORMANCES

Cities represent today the intrinsic socio-economic complexity of local systems. Looking at the performances of urban systems enable us to explaining the main factors of territorial development. By moving from the theory of "progressive systems", and assigning to the cities some of this theory's properties, it is possible to outline a methodological perspective to capture the emerging phenomena describing the cities' performances. Keeping this view in mind, the aim of the paper is facing the intrinsic socio-economic complexity and heterogeneity of cities within the EU integration policies.. In order to better qualify this issue, we provide a multidimensional scaling approach, as a quantitative method useful to compare the several urban performances by letting a cluster evidence among the EU cities emerge.Urban trajectories, progressive system, multidimensional scaling.