On the Alexander-Hirschowitz Theorem

The Alexander-Hirschowitz theorem says that a general collection of $k$ double points in ${\bf P}^n$ imposes independent conditions on homogeneous polynomials of degree $d$ with a well known list of exceptions. Alexander and Hirschowitz completed its proof in 1995, solving a long standing classical problem, connected with the Waring problem for polynomials. We expose a self-contained proof based mainly on previous works by Terracini, Hirschowitz, Alexander and Chandler, with a few simplifications. We claim originality only in the case $d=3$, where our proof is shorter. We end with an account of the history of the work on this problem.Comment: 29 pages, the proof in the case of cubics has been simplified, three references added, to appear in J. Pure Appl. Algebr

Semiclassical and quantum behavior of the Mixmaster model in the polymer approach for the isotropic Misner variable

We analyze the semiclassical and quantum behavior of the Bianchi IX Universe in the Polymer Quantum Mechanics framework, applied to the isotropic Misner variable, linked to the space volume of the model. The study is performed both in the Hamiltonian and field equations approaches, leading to the surprising result of a still singular and chaotic cosmology, whose Poincar\'e return map asymptotically overlaps the standard Belinskii-Khalatnikov-Lifshitz one. In the quantum sector, we reproduce the original analysis due to Misner, within the revised Polymer approach and we arrive to demonstrate that the quantum numbers of the point-Universe still remain constants of motion. This issue confirms the possibility to have quasi-classical states up to the initial singularity. The present study clearly demonstrates that the asymptotic behavior of the Bianchi IX Universe towards the singularity is not significantly affected by the Polymer reformulation of the spatial volume dynamics both on a pure quantum and a semiclassical level.Comment: 25 pages, 10 figures. v2: more discussions/clarification adde

One-loop topological expansion for spin glasses in the large connectivity limit

We apply for the first time a new one-loop topological expansion around the Bethe solution to the spin-glass model with field in the high connectivity limit, following the methodological scheme proposed in a recent work. The results are completely equivalent to the well known ones, found by standard field theoretical expansion around the fully connected model (Bray and Roberts 1980, and following works). However this method has the advantage that the starting point is the original Hamiltonian of the model, with no need to define an associated field theory, nor to know the initial values of the couplings, and the computations have a clear and simple physical meaning. Moreover this new method can also be applied in the case of zero temperature, when the Bethe model has a transition in field, contrary to the fully connected model that is always in the spin glass phase. Sharing with finite dimensional model the finite connectivity properties, the Bethe lattice is clearly a better starting point for an expansion with respect to the fully connected model. The present work is a first step towards the generalization of this new expansion to more difficult and interesting cases as the zero-temperature limit, where the expansion could lead to different results with respect to the standard one.Comment: 8 pages, 1 figur

Ensemble renormalization group for disordered systems

We propose and study a renormalization group transformation that can be used also for models with strong quenched disorder, like spin glasses. The method is based on a mapping between disorder distributions, chosen such as to keep some physical properties (e.g., the ratio of correlations averaged over the ensemble) invariant under the transformation. We validate this ensemble renormalization group by applying it to the hierarchical model (both the diluted ferromagnetic version and the spin glass version), finding results in agreement with Monte Carlo simulations.Comment: 7 pages, 10 figure

Security and Privacy in Resource-constrained Devices

Recent adversarial attacks have been shown IoT devices weaknesses due to their limited computing power. Given also their ubiquitous presence, lower costs and limitations in keeping security measures up-todate, resource-constrained devices represent a growing risk for the security of IT infrastructure. The scope of the research is to investigate the weaknesses of resource-constrained IoT devices. The methodology for the investigation is the legal analysis of existing legal frameworks regulating IoT cybersecurity and data security; afterwards it will be carried out a critical evaluation of the existing best practices. This critical analysis should face the twofold challenge of increasing transparency and trust in resource-constrained systems. Users and companies are two faces of the same coin: accountability of data collectors and user awareness are crucial in the security and data protection debate. Thus, a comprehensive overview of the relevant legal frameworks and guidelines would increase the understanding of risks of the users, whilst data controllers (especially of small and medium enterprises) may have an instrument to implement properly security measures

Security and Privacy in Resource-Constrained Devices

Recent adversarial attacks have been shown IoT devices weaknesses due to their limited computing power. Given also their ubiquitous presence, lower costs and limitations in keeping security measures up-todate, resource-constrained devices represent a growing risk for the security of IT infrastructure. The scope of the research is to investigate the weaknesses of resource-constrained IoT devices. The methodology for the investigation is the legal analysis of existing legal frameworks regulating IoT cybersecurity and data security; afterwards it will be carried out a critical evaluation of the existing best practices. This critical analysis should face the twofold challenge of increasing transparency and trust in resource-constrained systems. Users and companies are two faces of the same coin: accountability of data collectors and user awareness are crucial in the security and data protection debate. Thus, a comprehensive overview of the relevant legal frameworks and guidelines would increase the understanding of risks of the users, whilst data controllers (especially of small and medium enterprises) may have an instrument to implement properly security measures

The Unsecure Side of (Meta)Data in IoT Systems

The exponential spreading and deployment of emerging digital technologies such as the Internet of Things (IoT) has been remarkable: the IoT market is expected to triple, at least, from USD 170.57 billion in 2017 to USD 561.04 billion by 2022. IoT technologies collect, generate and communicate a huge amount of different data and metadata, through an increasing number of interconnected devices and sensors. Current EU legislation on data protection classifies data into personal and non-personal. The paper aims at charting the resulting entanglements from an interdisciplinary perspective. The legal analysis, integrated with a technical perspective, will address firstly the content of IoT communications, i.e. \u201cdata\u201d, and the underlying distinction between personal and non-personal. Secondly, the focus will shift on the metadata related to communications. Through a technical analysis of the highly sensitive nature of metadata, even when the content is encrypted, I will argue that metadata are likely to undermine even more the ontological and sharp division between personal and non-personal data upon which the European legal frameworks for privacy and data protection have been built. The incoming ePrivacy Regulation shall provide metadata, which should be considered always personal data, the same level of protection of \u201ccontent\u201d data. This interpretation might broaden the scope of application of GDPR and the connected obligations and responsibilities of data controllers and data processors too much

Magnetic properties of epsilon iron(III) oxide nanorod arrays functionalized with gold and copper(II) oxide

A sequential chemical vapor deposition (CVD) - radio frequency (RF)-sputtering approach was adopted to fabricate supported nanocomposites based on the scarcely investigated \u3b5-iron(III) oxide polymorph. In particular, \u3b5-Fe2O3 nanorod arrays were obtained by CVD, and their subsequent functionalization with Au and CuO nanoparticles (NPs) was carried out by RF-sputtering under mild operational conditions. Apart from a multi-technique characterization of material structure, morphology and chemical composition, particular efforts were dedicated to the investigation of their magnetic properties. The pertaining experimental data, discussed in relation to the system chemico-physical characteristics, are directly dependent on the actual chemical composition, as well as on the spatial distribution of Au and CuO nanoparticles. The approach adopted herein can be further implemented to control and tailor different morphologies and phase compositions of iron oxide-based nanomaterials, meeting thus the open requests of a variety of technological utilizations