Wick order, spreadability and exchangeability for monotone commutation relations

We exhibit a Hamel basis for the concrete $*$-algebra $\mathfrak{M}_o$ associated to monotone commutation relations realised on the monotone Fock space, mainly composed by Wick ordered words of annihilators and creators. We apply such a result to investigate spreadability and exchangeability of the stochastic processes arising from such commutation relations. In particular, we show that spreadability comes from a monoidal action implementing a dissipative dynamics on the norm closure $C^*$-algebra $\mathfrak{M} = \overline{\mathfrak{M}_o}$. Moreover, we determine the structure of spreadable and exchangeable monotone stochastic processes using their correspondence with sp\-reading invariant and symmetric monotone states, respectively.Comment: Ann. Henri Poincar\`e, to appea

On non-commutative spreadability

We review some results on spreadable quantum stochastic processes and present the structure of some monoids acting on the index-set of all integers Z. These semigroups are strictly related to spreadability, as the latter can be directly stated in terms of invariance with respect to their action. We are mainly focused on spreadable, Boolean, monotone, and q-deformed processes. In particular, we give a suitable version of the Ryll-Nardzewski Theorem in the aforementioned cases

Distributions for Nonsymmetric Monotone and Weakly Monotone Position Operators

We study the vacuum distribution, under an appropriate scaling, of a family of partial sums of nonsymmetric position operators on weakly monotone and monotone Fock spaces, respectively. We preliminary treat the case of weaklymonotone Fock space, and show that any single operator has the vacuum law belonging to the free Meixner class. After establishing some relations between the combinatorics of Motzkin and Riordan paths, we give a recursive formula for the vacuum moments of the law of any finite sum. Since the operators are monotone independent, the distribution is the monotone convolution of the free Meixner law above.We also investigate the asymptotic measure for these sums, which can be seen as “Poisson type” limit law. It turns out to belong to the free Meixner class, with an atomic and an absolutely continuous part (w.r.t. the Lebesgue measure). Finally, we briefly apply analogous considerations to the case of monotone Fock space

WEAKLY MONOTONE FOCK SPACE AND MONOTONE CONVOLUTION OF THE WIGNER LAW

We study the distribution (w.r.t. the vacuum state) of family of partial sums Sm of position operators on weakly monotone Fock space. We show that any single operator has the Wigner law, and an arbitrary family of them (with the index set linearly ordered) is a collection of monotone independent random variables. It turns out that our problem equivalently consists in nding the m-fold monotone convolution of the semicircle law. For m = 2 we compute the explicit distribution. For any m > 2 we give the moments of the measure, and show it is absolutely continuous and compactly supported on a symmetric interval whose endpoints can be found by a recurrence relation

Better virtual objects placement in real world through photogrammetry for object recognition and spatial anchoring

Augmented reality is one of the technologies, which in recent years has been most in the spotlight for communities as diverse as researchers, industrial actors and gamers. A common need in almost any scenarios is to “register” the virtual world with the real one, so that the right virtual objects can be accurately placed in the user's view. Although positioning could be aided by global systems such as GPS, there are situations in which its accuracy or feasibility cannot be guaranteed. Indeed, a few sectors could be prevented from exploring augmented reality as a disrupting technology if this need cannot be adequately fulfilled. In this work, photogrammetry is investigated for scenarios in which a few static already known and well-defined real-world objects can be used for anchoring in a broader area. The goal is to create a solid and reliable augmented reality framework in terms of precise placement of objects with the aim of using it in contexts where other solutions lack the required accuracy. In particular, this work considers as the primary use case a solution developed using Microsoft Hololens 2 for the positioning of digital objects in the context of railway maintenance by exploiting the recognition of real objects in the environment through photogrammetry techniques. Indeed, only a precise positioning of the objects will allow the pervasive diffusion of this technology in sectors such as health, military and in any case in all those contexts where accuracy and reliability are essential elements for ensuring safety of operations

A Review on Deep Learning Techniques for Railway Infrastructure Monitoring

In the last decade, thanks to a widespread diffusion of powerful computing machines, artificial intelligence has been attracting the attention of the academic and industrial worlds. This review aims to understand how the scientific community is approaching the use of deep-learning techniques in a particular industrial sector, the railway. This work is an in-depth analysis related to the last years of the way this new technology can try to provide answers even in a field where the primary requirement is to improve the already very high levels of safety. A strategic and constantly evolving field such as the railway sector could not remain extraneous to the use of this new and promising technology. Deep learning algorithms devoted to the classification, segmentation, and detection of the faults that affect the railway area and the overhead contact system are discussed. The railway sector offers many aspects that can be investigated with these techniques. This work aims to expose the possible applications of deep learning in the railway sector established on the type of recovered information and the type of algorithms to be used accordingly