The Italian primary school-size distribution and the city-size: a complex nexus

We characterize the statistical law according to which Italian primary school-size distributes. We find that the school-size can be approximated by a log-normal distribution, with a fat lower tail that collects a large number of very small schools. The upper tail of the school-size distribution decreases exponentially and the growth rates are distributed with a Laplace PDF. These distributions are similar to those observed for firms and are consistent with a Bose-Einstein preferential attachment process. The body of the distribution features a bimodal shape suggesting some source of heterogeneity in the school organization that we uncover by an in-depth analysis of the relation between schools-size and city-size. We propose a novel cluster methodology and a new spatial interaction approach among schools which outline the variety of policies implemented in Italy. Different regional policies are also discussed shedding lights on the relation between policy and geographical features.Comment: 16 pages, 10 figure

Hamiltonian mechanics on discrete manifolds

The mathematical/geometric structure of discrete models of systems, whether these models are obtained after discretization of a smooth system or as a direct result of modeling at the discrete level, have not been studied much. Mostly one is concerned regarding the nature of the solutions, but not much has been done regarding the structure of these discrete models. In this paper we provide a framework for the study of discrete models, speci?cally we present a Hamiltonian point of view. To this end we introduce the concept of a discrete calculus

Classical Tensors and Quantum Entanglement I: Pure States

The geometrical description of a Hilbert space asociated with a quantum system considers a Hermitian tensor to describe the scalar inner product of vectors which are now described by vector fields. The real part of this tensor represents a flat Riemannian metric tensor while the imaginary part represents a symplectic two-form. The immersion of classical manifolds in the complex projective space associated with the Hilbert space allows to pull-back tensor fields related to previous ones, via the immersion map. This makes available, on these selected manifolds of states, methods of usual Riemannian and symplectic geometry. Here we consider these pulled-back tensor fields when the immersed submanifold contains separable states or entangled states. Geometrical tensors are shown to encode some properties of these states. These results are not unrelated with criteria already available in the literature. We explicitly deal with some of these relations.Comment: 16 pages, 1 figure, to appear in Int. J. Geom. Meth. Mod. Phy

Coxiella burnetii Blocks Intracellular Interleukin-17 Signaling in Macrophages

Coxiella burnetii is an obligate intracellular bacterium and the etiological agent of Q fever. Successful host cell infection requires the Coxiella type IVB secretion system (T4BSS), which translocates bacterial effector proteins across the vacuole membrane into the host cytoplasm, where they manipulate a variety of cell processes. To identify host cell targets of Coxiella T4BSS effector proteins, we determined the transcriptome of murine alveolar macrophages infected with a Coxiella T4BSS effector mutant. We identified a set of inflammatory genes that are significantly upregulated in T4BSS mutant-infected cells compared to mock-infected cells or cells infected with wild-type (WT) bacteria, suggesting that Coxiella T4BSS effector proteins downregulate the expression of these genes. In addition, the interleukin-17 (IL-17) signaling pathway was identified as one of the top pathways affected by the bacteria. While previous studies demonstrated that IL-17 plays a protective role against several pathogens, the role of IL-17 during Coxiella infection is unknown. We found that IL-17 kills intracellular Coxiella in a dose-dependent manner, with the T4BSS mutant exhibiting significantly more sensitivity to IL-17 than WT bacteria. In addition, quantitative PCR confirmed the increased expression of IL-17 downstream signaling genes in T4BSS mutant-infected cells compared to WT- or mock-infected cells, including the proinflammatory cytokine genes Il1a, Il1b, and Tnfa, the chemokine genes Cxcl2 and Ccl5, and the antimicrobial protein gene Lcn2 We further confirmed that the Coxiella T4BSS downregulates macrophage CXCL2/macrophage inflammatory protein 2 and CCL5/RANTES protein levels following IL-17 stimulation. Together, these data suggest that Coxiella downregulates IL-17 signaling in a T4BSS-dependent manner in order to escape the macrophage immune response

Global Transformer Architecture for Indoor Room Temperature Forecasting

A thorough regulation of building energy systems translates in relevant energy savings and in a better comfort for the occupants. Algorithms to predict the thermal state of a building on a certain time horizon with a good confidence are essential for the implementation of effective control systems. This work presents a global Transformer architecture for indoor temperature forecasting in multi-room buildings, aiming at optimizing energy consumption and reducing greenhouse gas emissions associated with HVAC systems. Recent advancements in deep learning have enabled the development of more sophisticated forecasting models compared to traditional feedback control systems. The proposed global Transformer architecture can be trained on the entire dataset encompassing all rooms, eliminating the need for multiple room-specific models, significantly improving predictive performance, and simplifying deployment and maintenance. Notably, this study is the first to apply a Transformer architecture for indoor temperature forecasting in multi-room buildings. The proposed approach provides a novel solution to enhance the accuracy and efficiency of temperature forecasting, serving as a valuable tool to optimize energy consumption and decrease greenhouse gas emissions in the building sector