Vacuum condensates, flavor mixing and spontaneous supersymmetry breaking

Spontaneous supersymmetry (SUSY) breaking is revealed in all phenomena in which vacuum condensates are physically relevant. The dynamical breakdown of SUSY is generated by the condensates themselves, which lift the zero point energy. Evidence is presented in the case of the Wess-Zuimino model, and the flavor mixing case is treated in detail.Comment: 5 page

Vacuum condensates as a mechanism of spontaneous supersymmetry breaking

A possible mechanism for the spontaneous breaking of SUSY, based on the presence of vacuum condensates, is reviewed. Such a mechanism could occur in many physical examples, both at the fundamental and emergent level, and would be formally analogous to spontaneous SUSY breaking at finite temperature in the TFD formalism, in which case it can be applied as well. A possible experimental setup for detecting such a breaking through measurement of the Anandan-Aharonov invariants associated with vacuum condensates in an optical lattice model is proposed.Comment: 6 pages, 2 figures, review article to appear in the special issue "Supersymmetry, Supergravity, and Superstring Phenomenology" of Advances in High Energy Physic

Extracting the Italian output gap: a Bayesian approach

During the last decades particular effort has been directed towards understanding and predicting the relevant state of the business cycle with the objective of decomposing permanent shocks from those having only a transitory impact on real output. This trend--cycle decomposition has a relevant impact on several economic and fiscal variables and constitutes by itself an important indicator for policy purposes. This paper deals with trend--cycle decomposition for the Italian economy having some interesting peculiarities which makes it attractive to analyse from both a statistic and an historical perspective. We propose an univariate model for the quarterly real GDP, subsequently extended to include the price dynamics through a Phillips curve. This study considers a series of the Italian quarterly real GDP recently released by OECD which includes both the 1960s and the recent global financial crisis of 2007--2008. Parameters estimate as well as the signal extraction are performed within the Bayesian paradigm which effectively handles complex models where the parameters enter the log--likelihood function in a strongly nonlinear way. A new Adaptive Independent Metropolis--within--Gibbs sampler is then developed to efficiently simulate the parameters of the unobserved cycle. Our results suggest that inflation influences the Output Gap estimate, making the extracted Italian OG an important indicator of inflation pressures on the real side of the economy, as stated by the Phillips theory. Moreover, our estimate of the sequence of peaks and troughs of the Output Gap is in line with the OECD official dating of the Italian business cycle

Spontaneous Supersymmetry Breaking Induced by Vacuum Condensates

We propose a novel mechanism of spontaneous supersymmetry breaking which relies upon an ubiquitous feature of Quantum Field Theory, vacuum condensates. Such condensates play a crucial r\^{o}le in many phenomena. Examples include Unruh effect, superconductors, particle mixing, and quantum dissipative systems. We argue that in all these phenomena supersymmetry, when present, is spontaneously broken. Evidence for our conjecture is given for the Wess--Zumino model, that can be considered an approximation to the supersymmetric extensions of the above mentioned systems. The magnitude of the effect is estimated for a recently proposed experimental setup based on an optical lattice.Comment: 5 page

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

Mixing-induced Spontaneous Supersymmetry Breaking

It is conjectured that flavor mixing furnishes a universal mechanism for the spontaneous breaking of supersymmetry. The conjecture is proved explicitly for the mixing of two Wess--Zumino $\mathcal{N}=1$ supermultiplets and arguments for its general validity are given. The mechanism relies on the fact that, despite mixing treats fermions and bosons symmetrically, both the fermionic and the bosonic zero point energies are shifted by a positive amount and this kind of shift does not respect supersymmetry.Comment: 5 pages, 1 figure, Eq(12) of V1 corrected to Eq(22), explicit off-shell formulation included, one reference adde

Ricordo di Giuliano Marini

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