On the Logarithmic Asymptotics of the Sixth Painleve' Equation (Summer 2007)

We study the solutions of the sixth Painlev\'e equation with a logarithmic asymptotic behavior at a critical point. We compute the monodromy group associated to the solutions by the method of monodromy preserving deformations and we characterize the asymptotic behavior in terms of the monodromy itself.Comment: LaTeX with 8 figure

Brief Communication: Rapid mapping of landslide events: the 3 December 2013 Montescaglioso landslide, Italy

We present an approach to measure 3-D surface deformations caused by large, rapid-moving landslides using the amplitude information of high-resolution, X-band synthetic aperture radar (SAR) images. We exploit SAR data captured by the COSMO-SkyMed satellites to measure the deformation produced by the 3 December 2013 Montescaglioso landslide, southern Italy. The deformation produced by the deep-seated landslide exceeded 10 m and caused the disruption of a main road, a few homes and commercial buildings. The results open up the possibility of obtaining 3-D surface deformation maps shortly after the occurrence of large, rapid-moving landslides using high-resolution SAR data

Cyclic RGD peptidomimetics containing bifunctional diketopiperazine scaffolds as new potent integrin ligands

The synthesis of eight bifunctional diketopiperazine (DKP) scaffolds is described; these were formally derived from 2,3-diaminopropionic acid and aspartic acid (DKP-1-DKP-7) or glutamic acid (DKP-8) and feature an amine and a carboxylic acid functional group. The scaffolds differ in the configuration at the two stereocenters and the substitution at the diketopiperazinic nitrogen atoms. The bifunctional diketopiperazines were introduced into eight cyclic peptidomimetics containing the Arg-Gly-Asp (RGD) sequence. The resulting RGD peptidomimetics were screened for their ability to inhibit biotinylated vitronectin binding to the purified integrins \u3b1 v\u3b2 3 and \u3b1 v\u3b2 5, which are involved in tumor angiogenesis. Nanomolar IC 50 values were obtained for the RGD peptidomimetics derived from trans DKP scaffolds (DKP-2-DKP-8). Conformational studies of the cyclic RGD peptidomimetics by 1H NMR spectroscopy experiments (VT-NMR and NOESY spectroscopy) in aqueous solution and Monte Carlo/Stochastic Dynamics (MC/SD) simulations revealed that the highest affinity ligands display well-defined preferred conformations featuring intramolecular hydrogen-bonded turn motifs and an extended arrangement of the RGD sequence [C\u3b2(Arg)-C\u3b2(Asp) average distance 658.8 \uc5]. Docking studies were performed, starting from the representative conformations obtained from the MC/SD simulations and taking as a reference model the crystal structure of the extracellular segment of integrin \u3b1 v\u3b2 3 complexed with the cyclic pentapeptide, Cilengitide. The highest affinity ligands produced top-ranked poses conserving all the important interactions of the X-ray complex. Copyright \ua9 2012 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

Recurrence Plot Based Measures of Complexity and its Application to Heart Rate Variability Data

The knowledge of transitions between regular, laminar or chaotic behavior is essential to understand the underlying mechanisms behind complex systems. While several linear approaches are often insufficient to describe such processes, there are several nonlinear methods which however require rather long time observations. To overcome these difficulties, we propose measures of complexity based on vertical structures in recurrence plots and apply them to the logistic map as well as to heart rate variability data. For the logistic map these measures enable us not only to detect transitions between chaotic and periodic states, but also to identify laminar states, i.e. chaos-chaos transitions. The traditional recurrence quantification analysis fails to detect the latter transitions. Applying our new measures to the heart rate variability data, we are able to detect and quantify the laminar phases before a life-threatening cardiac arrhythmia occurs thereby facilitating a prediction of such an event. Our findings could be of importance for the therapy of malignant cardiac arrhythmias

Holonomy of the Ising model form factors

We study the Ising model two-point diagonal correlation function $C(N,N)$ by presenting an exponential and form factor expansion in an integral representation which differs from the known expansion of Wu, McCoy, Tracy and Barouch. We extend this expansion, weighting, by powers of a variable $\lambda$, the $j$-particle contributions, $f^{(j)}_{N,N}$. The corresponding $\lambda$ extension of the two-point diagonal correlation function, $C(N,N; \lambda)$, is shown, for arbitrary $\lambda$, to be a solution of the sigma form of the Painlev{\'e} VI equation introduced by Jimbo and Miwa. Linear differential equations for the form factors $f^{(j)}_{N,N}$ are obtained and shown to have both a ``Russian doll'' nesting, and a decomposition of the differential operators as a direct sum of operators equivalent to symmetric powers of the differential operator of the elliptic integral $E$. Each $f^{(j)}_{N,N}$ is expressed polynomially in terms of the elliptic integrals $E$ and $K$. The scaling limit of these differential operators breaks the direct sum structure but not the ``Russian doll'' structure. The previous $\lambda$-extensions, $C(N,N; \lambda)$ are, for singled-out values $\lambda= \cos(\pi m/n)$ ($m, n$ integers), also solutions of linear differential equations. These solutions of Painlev\'e VI are actually algebraic functions, being associated with modular curves.Comment: 39 page

INTEGRIN AND CADHERIN LIGANDS: INTERACTION STUDIES BY COMPUTATIONAL METHODS AND BIOAFFINITY NMR ON INTACT CELLS

On a molecular level protein \u2013 ligand interactions are central to a number of biological processes, but their investigation is inherently difficult due to several problems, especially for membrane proteins. The study of this type of interactions poses a whole set of challenges, including the characterization of the dynamic behaviour and of the conformational properties of the ligands in complex with the target macromolecules. A variety of biophysical methods have been developed to study protein \u2013 ligand interactions and several NMR spectroscopic techniques have emerged as powerful methods to identify and characterize the binding of ligands with receptor proteins. Ligand-based methods do not require labeled protein, since only the ligand NMR signals are detected and only a small amount of protein is required. These techniques are particularly useful in the medium\u2013low affinity range and, therefore they have been adopted to detect ligand interactions in various systems. Among the ligand-based NMR techniques, Saturation Transfer Difference (STD) and transferred-NOE focus on the NMR signals of the ligand and utilize NOE effects between protein and ligand. They are used for: i) the definition of the bioactive conformation of the ligand in the bound state (tr-NOESY), ii) the identification and characterization of the binding mode of the ligand to the receptor with epitope mapping of the ligand itself (STD). The use of the technique is limited to molecules that exhibit a dissociation constant Kd between 10-3 M and 10-7 M. During my PhD, I had the highly qualifying opportunity to grasp these new potent NMR methods, and to apply them for assessing the interactions of cell surface proteins with peptidomimetics. Since membrane proteins, such as integrins, change their conformation if extracted from their environment, it is clear the importance of working in the biophysical neighbourhood of the membrane itself and not in an isotropic extracellular medium. For this reason, when appropriate to the project, I have carried out NMR experiments using intact cells overexpressing the proteins of interest. Specifically, two main topics have been addressed: 1. The first and second year of my PhD have been mainly focused on the conformational study of peptidomimetic integrin ligands and on the investigation of their interaction with platelets and cancer cell overexpressing integrins on their membrane. This study has been developed within the framework of a PRIN project (MIUR-PRIN project 2010NRREPL \u201cSynthesis and Biomedical Applications of Tumor-Targeting Peptidomimetics\u201d) in collaboration with the research groups of Proff. Gennari and Piarulli (University of Insubria) as regards the synthetic activities and with the group of Dr. Belvisi as regards the computational and design studies. 2. The second part of my PhD was mainly focused on cadherins, a class of cell adhesion proteins that promote homophilic interactions. This work is at an early stage and has been developed within the framework of a FIRB project coordinated by Dr. Civera (MIUR-FIRB \u201cFuturo in Ricerca\u201d RBFR088ITV \u201cComputer-aided design, synthesis and biological evaluation of peptidomimetics targeting N-cadherin as anticancer agents\u201d). The NMR study has been aimed at obtaining a thorough understanding of the interaction of peptidomimetic molecules with isolated cadherin constructs containing relevant extracellular domains

Regional prediction of landslide hazard using probability analysis of intense rainfall in the Hoa Binh province, Vietnam.

The main objective of this study is to assess regional landslide hazards in the Hoa Binh province of Vietnam. A landslide inventory map was constructed from various sources with data mainly for a period of 21 years from 1990 to 2010. The historic inventory of these failures shows that rainfall is the main triggering factor in this region. The probability of the occurrence of episodes of rainfall and the rainfall threshold were deduced from records of rainfall for the aforementioned period. The rainfall threshold model was generated based on daily and cumulative values of antecedent rainfall of the landslide events. The result shows that 15-day antecedent rainfall gives the best fit for the existing landslides in the inventory. The rainfall threshold model was validated using the rainfall and landslide events that occurred in 2010 that were not considered in building the threshold model. The result was used for estimating temporal probability of a landslide to occur using a Poisson probability model. Prior to this work, five landslide susceptibility maps were constructed for the study area using support vector machines, logistic regression, evidential belief functions, Bayesian-regularized neural networks, and neuro-fuzzy models. These susceptibility maps provide information on the spatial prediction probability of landslide occurrence in the area. Finally, landslide hazard maps were generated by integrating the spatial and the temporal probability of landslide. A total of 15 specific landslide hazard maps were generated considering three time periods of 1, 3, and 5 years

Non-susceptible landslide areas in Italy and in the Mediterranean region

Abstract. We used landslide information for 13 study areas in Italy and morphometric information obtained from the 3-arcseconds shuttle radar topography mission digital elevation model (SRTM DEM) to determine areas where landslide susceptibility is expected to be negligible in Italy and in the landmasses surrounding the Mediterranean Sea. The morphometric information consisted of the local terrain slope which was computed in a square 3 × 3-cell moving window, and in the regional relative relief computed in a circular 15 × 15-cell moving window. We tested three different models to classify the "non-susceptible" landslide areas, including a linear model (LNR), a quantile linear model (QLR), and a quantile, non-linear model (QNL). We tested the performance of the three models using independent landslide information presented by the Italian Landslide Inventory (Inventario Fenomeni Franosi in Italia – IFFI). Best results were obtained using the QNL model. The corresponding zonation of non-susceptible landslide areas was intersected in a geographic information system (GIS) with geographical census data for Italy. The result determined that 57.5% of the population of Italy (in 2001) was located in areas where landslide susceptibility is expected to be negligible. We applied the QNL model to the landmasses surrounding the Mediterranean Sea, and we tested the synoptic non-susceptibility zonation using independent landslide information for three study areas in Spain. Results showed that the QNL model was capable of determining where landslide susceptibility is expected to be negligible in the validation areas in Spain. We expect our results to be applicable in similar study areas, facilitating the identification of non-susceptible landslide areas, at the synoptic scale

Fuchs versus Painlev\'e

We briefly recall the Fuchs-Painlev\'e elliptic representation of Painlev\'e VI. We then show that the polynomiality of the expressions of the correlation functions (and form factors) in terms of the complete elliptic integral of the first and second kind, $K$ and $E$, is a straight consequence of the fact that the differential operators corresponding to the entries of Toeplitz-like determinants, are equivalent to the second order operator $L_E$ which has $E$ as solution (or, for off-diagonal correlations to the direct sum of $L_E$ and $d/dt$). We show that this can be generalized, mutatis mutandis, to the anisotropic Ising model. The singled-out second order linear differential operator $L_E$ being replaced by an isomonodromic system of two third-order linear partial differential operators associated with $\Pi_1$, the Jacobi's form of the complete elliptic integral of the third kind (or equivalently two second order linear partial differential operators associated with Appell functions, where one of these operators can be seen as a deformation of $L_E$). We finally explore the generalizations, to the anisotropic Ising models, of the links we made, in two previous papers, between Painlev\'e non-linear ODE's, Fuchsian linear ODE's and elliptic curves. In particular the elliptic representation of Painlev\'e VI has to be generalized to an ``Appellian'' representation of Garnier systems.Comment: Dedicated to the : Special issue on Symmetries and Integrability of Difference Equations, SIDE VII meeting held in Melbourne during July 200