Boundary operators in minimal Liouville gravity and matrix models

We interpret the matrix boundaries of the one matrix model (1MM) recently constructed by two of the authors as an outcome of a relation among FZZT branes. In the double scaling limit, the 1MM is described by the (2,2p+1) minimal Liouville gravity. These matrix operators are shown to create a boundary with matter boundary conditions given by the Cardy states. We also demonstrate a recursion relation among the matrix disc correlator with two different boundaries. This construction is then extended to the two matrix model and the disc correlator with two boundaries is compared with the Liouville boundary two point functions. In addition, the realization within the matrix model of several symmetries among FZZT branes is discussed.Comment: 26 page

Enumeration of maps with self avoiding loops and the O(n) model on random lattices of all topologies

We compute the generating functions of a O(n) model (loop gas model) on a random lattice of any topology. On the disc and the cylinder, they were already known, and here we compute all the other topologies. We find that the generating functions (and the correlation functions of the lattice) obey the topological recursion, as usual in matrix models, i.e they are given by the symplectic invariants of their spectral curve.Comment: pdflatex, 89 pages, 12 labelled figures (15 figures at all), minor correction

An integrated modelling framework from cells to organism based on a cohort of digital embryos

We conducted a quantitative comparison of developing sea urchin embryos based on the analysis of five digital specimens obtained by automatic processing of in toto 3D+ time image data. These measurements served the reconstruction of a prototypical cell lineage tree able to predict the spatiotemporal cellular organisation of a normal sea urchin blastula. The reconstruction was achieved by designing and tuning a multi-level probabilistic model that reproduced embryo-level dynamics from a small number of statistical parameters characterising cell proliferation, cell surface area and cell volume evolution along the cell lineage. Our resulting artificial prototype was embedded in 3D space by biomechanical agent-based modelling and simulation, which allowed a systematic exploration and optimisation of free parameters to fit the experimental data and test biological hypotheses. The spherical monolayered blastula and the spatial arrangement of its different cell types appeared tightly constrained by cell stiffness, cell-adhesion parameters and blastocoel turgor pressure

Beyond LLM in M-theory

The Lin, Lunin, Maldacena (LLM) ansatz in D = 11 supports two independent Killing directions when a general Killing spinor ansatz is considered. Here we show that these directions always commute, identify when the Killing spinors are charged, and show that both their inner product and resulting geometry are governed by two fundamental constants. In particular, setting one constant to zero leads to AdS7 x S4, setting the other to zero gives AdS4 x S7, while flat spacetime is recovered when both these constants are zero. Furthermore, when the constants are equal, the spacetime is either LLM, or it corresponds to the Kowalski-Glikman solution where the constants are simply the mass parameter.Comment: 1+30 pages, footnote adde

FZZT Brane Relations in the Presence of Boundary Magnetic Fields

We show how a boundary state different from the (1,1) Cardy state may be realised in the (m,m+1) minimal string by the introduction of an auxiliary matrix into the standard two hermitian matrix model. This boundary is a natural generalisation of the free spin boundary state in the Ising model. The resolvent for the auxiliary matrix is computed using an extension of the saddle-point method of Zinn-Justin to the case of non-identical potentials. The structure of the saddle-point equations result in a Seiberg-Shih like relation between the boundary states which is valid away from the continuum limit, in addition to an expression for the spectral curve of the free spin boundary state. We then show how the technique may be used to analyse boundary states corresponding to a boundary magnetic field, thereby allowing us to generalise the work of Carroll et al. on the boundary renormalisation flow of the Ising model, to any (m,m+1) model.Comment: 23 pages, 5 figures (3 new). Two new sections added giving examples of the construction. Explanations clarified. Minor changes to the conclusion but main results unchanged. Matches published versio

The GAIA theory: from Lovelock to Margulis. From a homeostatic to a cognitive autopoietic worldview

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A Digital Framework to Build, Visualize and Analyze a Gene Expression Atlas with Cellular Resolution in Zebrafish Early Embryogenesis

A gene expression atlas is an essential resource to quantify and understand the multiscale processes of embryogenesis in time and space. The automated reconstruction of a prototypic 4D atlas for vertebrate early embryos, using multicolor fluorescence in situ hybridization with nuclear counterstain, requires dedicated computational strategies. To this goal, we designed an original methodological framework implemented in a software tool called Match-IT. With only minimal human supervision, our system is able to gather gene expression patterns observed in different analyzed embryos with phenotypic variability and map them onto a series of common 3D templates over time, creating a 4D atlas. This framework was used to construct an atlas composed of 6 gene expression templates from a cohort of zebrafish early embryos spanning 6 developmental stages from 4 to 6.3 hpf (hours post fertilization). They included 53 specimens, 181,415 detected cell nuclei and the segmentation of 98 gene expression patterns observed in 3D for 9 different genes. In addition, an interactive visualization software, Atlas-IT, was developed to inspect, supervise and analyze the atlas. Match-IT and Atlas-IT, including user manuals, representative datasets and video tutorials, are publicly and freely available online. We also propose computational methods and tools for the quantitative assessment of the gene expression templates at the cellular scale, with the identification, visualization and analysis of coexpression patterns, synexpression groups and their dynamics through developmental stages

Inducible Caspase9-mediated suicide gene for MSC-based cancer gene therapy

Cellular therapies based on mesenchymal stromal/stem cells (MSC) are promising strategies in regenerative medicine and oncology. Despite encouraging results, there is still some level of concerns on inoculating MSC in cancer patients. To face this issue, one possibility resides in engineering MSC by incorporating a suicide gene in order to control their fate once infused. Strategies based on Herpes Simplex Virus Thymidine Kinase (HSV-TK) and the Cytosine Deaminase genes have been developed and more recently a novel suicide gene, namely, iCasp9, has been proposed. This approach is based on a variant of human Caspase9 that binds with high affinity to a synthetic, bioinert small molecule (AP20187) leading to cell death. Based on this technology so far marginally applied to MSC, we tested the suitability of iCasp9 suicide strategy in MSC to further increase their safety. MSC have been transfected by a lentiviral vector carrying iCasp9 gene and then tested for viability after AP20187 treatment in comparison with mock-transfected cells. Moreover, accounting our anti-tumor approaches based on MSC expressing potent anti-cancer ligand TNF-Related Apoptosis-Inducing Ligand (TRAIL), we generated adipose MSC co-expressing iCasp9 and TRAIL successfully targeting an aggressive sarcoma type. These data show that anti-cancer and suicide mechanisms can coexist without affecting cells performance and hampering the tumoricidal activity mediated by TRAIL. In conclusion, this study originally indicates the suitability of combining a MSC-based anti-cancer gene approach with iCasp9 demonstrating efficiency and specificity