Bipartite quantum states and random complex networks

We introduce a mapping between graphs and pure quantum bipartite states and show that the associated entanglement entropy conveys non-trivial information about the structure of the graph. Our primary goal is to investigate the family of random graphs known as complex networks. In the case of classical random graphs we derive an analytic expression for the averaged entanglement entropy $\bar S$ while for general complex networks we rely on numerics. For large number of nodes $n$ we find a scaling $\bar{S} \sim c \log n +g_e$ where both the prefactor $c$ and the sub-leading O(1) term $g_e$ are a characteristic of the different classes of complex networks. In particular, $g_e$ encodes topological features of the graphs and is named network topological entropy. Our results suggest that quantum entanglement may provide a powerful tool in the analysis of large complex networks with non-trivial topological properties.Comment: 4 pages, 3 figure

Meta-modeling on detailed geography for accurate prediction of invasive alien species dispersal

Invasive species are recognized as a significant threat to biodiversity. The mathematical modeling of their spatio-temporal dynamics can provide significant help to environmental managers in devising suitable control strategies. Several mathematical approaches have been proposed in recent decades to efficiently model the dispersal of invasive species. Relying on the assumption that the dispersal of an individual is random, but the density of individuals at the scale of the population can be considered smooth, reaction-diffusion models are a good trade-off between model complexity and flexibility for use in different situations. In this paper we present a continuous reaction-diffusion model coupled with arbitrary Polynomial Chaos (aPC) to assess the impact of uncertainties in the model parameters. We show how the finite elements framework is well-suited to handle important landscape heterogeneities as elevation and the complex geometries associated with the boundaries of an actual geographical region. We demonstrate the main capabilities of the proposed coupled model by assessing the uncertainties in the invasion of an alien species invading the Basque Country region in Northern Spain

Modeling cardiac structural heterogeneity via space-fractional differential equations

We discuss here the use of non-local models in space and fractional order operators in the characterisation of structural complexity and the modeling of propagation in heterogeneous biological tissues. In the specific, we consider the application of space-fractional operators in the context of cardiac electrophysiology, where the lack of clear separation of scales of the highly heterogeneous myocardium triggers peculiar features such as the dispersion of action potential duration, that have been observed experimentally, but cannot be described by the standard monodomain or bidomain models. We describe the methodology and compare the results of a standard monodomain model with results of a model with a non-local component in space

Discretizations of the spectral fractional Laplacian on general domains with Dirichlet, Neumann, and Robin boundary conditions

In this work, we propose novel discretisations of the spectral fractional Laplacian on bounded domains based on the integral formulation of the operator via the heat-semigroup formalism. Specifically, we combine suitable quadrature formulas of the integral with a finite element method for the approximation of the solution of the corresponding heat equation. We derive two families of discretisations with order of convergence depending on the regularity of the domain and the function on which the fractional Laplacian is acting. Unlike other existing approaches in literature, our method does not require the computation of the eigenpairs of the Laplacian on the considered domain, can be implemented on possibly irregular bounded domains, and can naturally handle different types of boundary constraints. Various numerical simulations are provided to illustrate performance of the proposed method and support our theoretical results.FdT acknowledges support of Toppforsk project Waves and Nonlinear Phenomena (WaNP), grant no. 250070 from the Research Council of Norway. ERCIM ``Alain Benoussan" Fellowship programm

From early stress to 12-month development in very preterm infants: Preliminary findings on epigenetic mechanisms and brain growth

Very preterm (VPT) infants admitted to Neonatal Intensive Care Unit (NICU) are at risk for altered brain growth and less-than-optimal socio-emotional development. Recent research suggests that early NICU-related stress contributes to socio-emotional impairments in VPT infants at 3 months through epigenetic regulation (i.e., DNA methylation) of the serotonin transporter gene (SLC6A4). In the present longitudinal study we assessed: (a) the effects of NICU-related stress and SLC6A4 methylation variations from birth to discharge on brain development at term equivalent age (TEA); (b) the association between brain volume at TEA and socio-emotional development (i.e., Personal-Social scale of Griffith Mental Development Scales, GMDS) at 12 months corrected age (CA). Twenty-four infants had complete data at 12-month-age. SLC6A4 methylation was measured at a specific CpG previously associated with NICU-related stress and socio-emotional stress. Findings confirmed that higher NICU-related stress associated with greater increase of SLC6A4 methylation at NICU discharge. Moreover, higher SLC6A4 discharge methylation was associated with reduced anterior temporal lobe (ATL) volume at TEA, which in turn was significantly associated with less-than-optimal GMDS Personal-Social scale score at 12 months CA. The reduced ATL volume at TEA mediated the pathway linking stress-related increase in SLC6A4 methylation at NICU discharge and socio-emotional development at 12 months CA. These findings suggest that early adversity-related epigenetic changes might contribute to the long-lasting programming of socio-emotional development in VPT infants through epigenetic regulation and structural modifications of the developing brain

Natural history and risk factors for diabetic kidney disease in patients with T2D: lessons from the AMD-annals

The Associazione Medici Diabetologi (AMD) annals initiative is an ongoing observational survey promoted by AMD. It is based on a public network of about 700 Italian diabetes clinics, run by specialists who provide diagnostic confirmation and prevention and treatment of diabetes and its complications. Over the last few years, analysis of the AMD annals dataset has contributed several important insights on the clinical features of type-2 diabetes kidney disease and their prognostic and therapeutic implications. First, non-albuminuric renal impairment is the predominant clinical phenotype. Even though associated to a lower risk of progression compared to overt albuminuria, it contributes significantly to the burden of end-stage renal disease morbidity. Second, optimal blood pressure control provides significant but incomplete renal protection. It reduces albuminuria but there may be a J curve phenomenon with eGFR at very low blood pressure values. Third, hyperuricemia and diabetic hyperlipidemia, namely elevated triglycerides and low HDL cholesterol, are strong independent predictors of chronic kidney disease (CKD) onset in diabetes, although the pathogenetic mechanisms underlying these associations remain uncertain. Fourth, the long-term intra-individual variability in HbA1c, lipid parameters, uric acid and blood pressure plays a greater role in the appearance and progression of CKD than the absolute value of each single variable. These data help clarify the natural history of CKD in patients with type 2 diabetes and provide important clues for designing future interventional studies

Ground state fidelity and quantum phase transitions in free Fermi systems

We compute the fidelity between the ground states of general quadratic fermionic hamiltonians and analyze its connections with quantum phase transitions. Each of these systems is characterized by a $L\times L$ real matrix whose polar decomposition, into a non-negative $\Lambda$ and a unitary $T$, contains all the relevant ground state (GS) information. The boundaries between different regions in the GS phase diagram are given by the points of, possibly asymptotic, singularity of $\Lambda$. This latter in turn implies a critical drop of the fidelity function. We present general results as well as their exemplification by a model of fermions on a totally connected graph.Comment: 4 pages, 2 figure