Reduction of pre-Hamiltonian actions

We prove a reduction theorem for the tangent bundle of a Poisson manifold $(M, \pi)$ endowed with a pre-Hamiltonian action of a Poisson Lie group $(G, \pi_G)$. In the special case of a Hamiltonian action of a Lie group, we are able to compare our reduction to the classical Marsden-Ratiu reduction of $M$. If the manifold $M$ is symplectic and simply connected, the reduced tangent bundle is integrable and its integral symplectic groupoid is the Marsden-Weinstein reduction of the pair groupoid $M \times \bar{M}$.Comment: 18 pages, final version, to appear in Journal of Geometry and Physic

Hybridized tetraquarks

We propose a new interpretation of the neutral and charged X,Z exotic hadron resonances. Hybridized-tetraquarks are neither purely compact tetraquark states nor bound or loosely bound molecules but rather a manifestation of the interplay between the two. While meson molecules need a negative or zero binding energy, its counterpart for h -tetraquarks is required to be positive. The formation mechanism of this new class of hadrons is inspired by that of Feshbach metastable states in atomic physics. The recent claim of an exotic resonance in the View the MathML source channel by the D0 Collaboration and the negative result presented subsequently by the LHCb Collaboration are understood in this scheme, together with a considerable portion of available data on X,Z particles. Considerations on a state with the same quantum numbers as the X(5568) are also made

Visualizing and Understanding Sum-Product Networks

Sum-Product Networks (SPNs) are recently introduced deep tractable probabilistic models by which several kinds of inference queries can be answered exactly and in a tractable time. Up to now, they have been largely used as black box density estimators, assessed only by comparing their likelihood scores only. In this paper we explore and exploit the inner representations learned by SPNs. We do this with a threefold aim: first we want to get a better understanding of the inner workings of SPNs; secondly, we seek additional ways to evaluate one SPN model and compare it against other probabilistic models, providing diagnostic tools to practitioners; lastly, we want to empirically evaluate how good and meaningful the extracted representations are, as in a classic Representation Learning framework. In order to do so we revise their interpretation as deep neural networks and we propose to exploit several visualization techniques on their node activations and network outputs under different types of inference queries. To investigate these models as feature extractors, we plug some SPNs, learned in a greedy unsupervised fashion on image datasets, in supervised classification learning tasks. We extract several embedding types from node activations by filtering nodes by their type, by their associated feature abstraction level and by their scope. In a thorough empirical comparison we prove them to be competitive against those generated from popular feature extractors as Restricted Boltzmann Machines. Finally, we investigate embeddings generated from random probabilistic marginal queries as means to compare other tractable probabilistic models on a common ground, extending our experiments to Mixtures of Trees.Comment: Machine Learning Journal paper (First Online), 24 page

“FADN - FER system description and its exploitability in Agricultural Policies impact evaluation: the system can accept further development specification in order to assist Policies design and evaluation?”

In this paper we examined subsides received from actions set in motion by the two Pillars of EU Structural Policies. Data come from Fadn-Fer system that collects a large number of variables regarding results and economical behaviour of farmers active in the rural areas, including business and public entrepreneurs. Both FADN register and FER questionnaire collect data on CAP and RD contributes received to perform activities proposed by CAP/RD Pillars and measures; then FADN -FER databases can be used for Policies evaluation exercises as well as to improve Policies’ design and targets. The available vectors of data have been analyzed through an approach that aims to represent the principal financial records and figures of the EU structural policies in two cycles: the first period for the cycle 2000-2006 and the second period for the first two years of the cycle 2007-2013.Policies Evaluation, subsidies, type of farming, Agricultural and Food Policy, Q18, R11.,

Macroscopic description of microscopically strongly inhomogenous systems: A mathematical basis for the synthesis of higher gradients metamaterials

We consider the time evolution of a one dimensional $n$-gradient continuum. Our aim is to construct and analyze discrete approximations in terms of physically realizable mechanical systems, called microscopic because they are living on a smaller space scale. We validate our construction by proving a convergence theorem of the microscopic system to the given continuum, as the scale parameter goes to zero.Comment: 20 page

The dynamics of French public debt: Paths for fiscal consolidations

We analyze possible targets for the French debt-to-GDP ratio with a small model. The role of the US and German GDP growth, prices of raw materials, ECB monetary policy, and domestic policy is analyzed in the debt dynamics. We find that external conditions, together with policies to stimulate growth and to generate a government surplus, play a fundamental role in the French fiscal consolidation.Debt to GDP Ratio, French Economy, International Factors

Non-stationary inflation and panel estimates of the n ew Keynesian Phillips curve for Australia

This paper uses a recent panel method of Russell and Banerjee (2008) to estimate the new Keynesian Phillips curve for Australia. Our estimates show that while the hybrid new Keynesian Phillips curve and backward looking conventional Phillips curve are well determined, estimates of the Phillips curve with the pure forward looking expectations are unsatisfactory.Panel data estimates, new Keynesian Phillips curve, Australia and Unit roots in the rate of inflation.

The dynamics of Spanish public debt and sustainable paths for fiscal consolidation

This paper analyses possible patterns for the Spain debt-to-GDP ratio with a small macroeconomic model. The role of international macroeconomic variables (such as the US and French GDP growth rates, prices of raw materials, ECB monetary policy stance) and domestic policy instruments is analyzed in the debt dynamics. We find that external conditions, together with policies aimed to stimulate the growth and fulfilling Maastricht restrictions on deficit, play a fundamental role for fiscal consolidation in Spain and help to reach a sustainable pattern.Debt to GDP Ratio, Spain Economy, International Factors, SUR