Multitasking associative networks

We introduce a bipartite, diluted and frustrated, network as a sparse restricted Boltzman machine and we show its thermodynamical equivalence to an associative working memory able to retrieve multiple patterns in parallel without falling into spurious states typical of classical neural networks. We focus on systems processing in parallel a finite (up to logarithmic growth in the volume) amount of patterns, mirroring the low-level storage of standard Amit-Gutfreund-Sompolinsky theory. Results obtained trough statistical mechanics, signal-to-noise technique and Monte Carlo simulations are overall in perfect agreement and carry interesting biological insights. Indeed, these associative networks pave new perspectives in the understanding of multitasking features expressed by complex systems, e.g. neural and immune networks.Comment: to appear on Phys.Rev.Let

An automated fluorescence videomicroscopy assay for the detection of mitotic catastrophe

Mitotic catastrophe can be defined as a cell death mode that occurs during or shortly after a prolonged/aberrant mitosis, and can show apoptotic or necrotic features. However, conventional procedures for the detection of apoptosis or necrosis, including biochemical bulk assays and cytofluorometric techniques, cannot discriminate among pre-mitotic, mitotic and post-mitotic death, and hence are inappropriate to monitor mitotic catastrophe. To address this issue, we generated isogenic human colon carcinoma cell lines that differ in ploidy and p53 status, yet express similar amounts of fluorescent biosensors that allow for the visualization of chromatin (histone H2B coupled to green fluorescent protein (GFP)) and centrosomes (centrin coupled to the Discosoma striata red fluorescent protein (DsRed)). By combining high-resolution fluorescence videomicroscopy and automated image analysis, we established protocols and settings for the simultaneous assessment of ploidy, mitosis, centrosome number and cell death (which in our model system occurs mainly by apoptosis). Time-lapse videomicroscopy showed that this approach can be used for the high-throughput detection of mitotic catastrophe induced by three mechanistically distinct anti-mitotic agents (dimethylenastron (DIMEN), nocodazole (NDZ) and paclitaxel (PTX)), and – in this context – revealed an important role of p53 in the control of centrosome number

Parallel processing in immune networks

In this work we adopt a statistical mechanics approach to investigate basic, systemic features exhibited by adaptive immune systems. The lymphocyte network made by B-cells and T-cells is modeled by a bipartite spin-glass, where, following biological prescriptions, links connecting B-cells and T-cells are sparse. Interestingly, the dilution performed on links is shown to make the system able to orchestrate parallel strategies to fight several pathogens at the same time; this multitasking capability constitutes a remarkable, key property of immune systems as multiple antigens are always present within the host. We also define the stochastic process ruling the temporal evolution of lymphocyte activity, and show its relaxation toward an equilibrium measure allowing statistical mechanics investigations. Analytical results are compared with Monte Carlo simulations and signal-to-noise outcomes showing overall excellent agreement. Finally, within our model, a rationale for the experimentally well-evidenced correlation between lymphocytosis and autoimmunity is achieved; this sheds further light on the systemic features exhibited by immune networks.Comment: 21 pages, 9 figures; to appear in Phys. Rev.

Analogue neural networks on correlated random graphs

We consider a generalization of the Hopfield model, where the entries of patterns are Gaussian and diluted. We focus on the high-storage regime and we investigate analytically the topological properties of the emergent network, as well as the thermodynamic properties of the model. We find that, by properly tuning the dilution in the pattern entries, the network can recover different topological regimes characterized by peculiar scalings of the average coordination number with respect to the system size. The structure is also shown to exhibit a large degree of cliquishness, even when very sparse. Moreover, we obtain explicitly the replica symmetric free energy and the self-consistency equations for the overlaps (order parameters of the theory), which turn out to be classical weighted sums of 'sub-overlaps' defined on all possible sub-graphs. Finally, a study of criticality is performed through a small-overlap expansion of the self-consistencies and through a whole fluctuation theory developed for their rescaled correlations: Both approaches show that the net effect of dilution in pattern entries is to rescale the critical noise level at which ergodicity breaks down.Comment: 34 pages, 3 figure

The Way of Water: ALMA resolves H2O emission lines in a strongly lensed dusty star-forming galaxy at z ∼\sim 3.1

We report ALMA high-resolution observations of water emission lines $p-{\rm{H_2O}} (2_{02}-1_{11}$), $o-{\rm{H_2O}} (3_{21}-3_{12})$, $p-{\rm{H_2O}} (4_{22}-4_{13})$, in the strongly lensed galaxy HATLASJ113526.2-01460 at redshift z $\sim$ 3.1. From the lensing-reconstructed maps of water emission and line profiles, we infer the general physical properties of the ISM in the molecular clouds where the lines arise. We find that the water vapor lines $o-{\rm{H_2O}} (3_{21}-3_{12})$, $p-{\rm{H_2O}} (4_{22}-4_{13})$ are mainly excited by FIR pumping from dust radiation in a warm and dense environment, with dust temperatures ranging from 70 K to $\sim 100$ K, as suggested by the line ratios. The $p-{\rm{H_2O}} (2_{02}-1_{11})$ line instead, is excited by a complex interplay between FIR pumping and collisional excitation in the dense core of the star-forming region. This scenario is also supported by the detection of the medium-level excitation of CO resulting in the line emission CO (J=8-7). Thanks to the unprecedented high resolution offered by the combination of ALMA capabilities and gravitational lensing, we discern the different phases of the ISM and locate the hot molecular clouds into a physical scale of $\sim$ 500 pc. We discuss the possibility of J1135 hosting an AGN in its accretion phase. Finally, we determine the relation between the water emission lines and the total IR luminosity of J1135, as well as the SFR as a function of water emission intensities, comparing the outcomes to local and high-$z$ galactic samples from the literature.Comment: 23 pages, 13 figures, to be published in Astrophysical Journa

The Geometry and Moduli of K3 Surfaces

These notes will give an introduction to the theory of K3 surfaces. We begin with some general results on K3 surfaces, including the construction of their moduli space and some of its properties. We then move on to focus on the theory of polarized K3 surfaces, studying their moduli, degenerations and the compactification problem. This theory is then further enhanced to a discussion of lattice polarized K3 surfaces, which provide a rich source of explicit examples, including a large class of lattice polarizations coming from elliptic fibrations. Finally, we conclude by discussing the ample and Kahler cones of K3 surfaces, and give some of their applications.Comment: 34 pages, 2 figures. (R. Laza, M. Schutt and N. Yui, eds.