Singular inextensible limit in the vibrations of post-buckled rods: Analytical derivation and role of boundary conditions

In-plane vibrations of an elastic rod clamped at both extremities are studied. The rod is modeled as an extensible planar Kirchhoff elastic rod under large displacements and rotations. Equilibrium configurations and vibrations around these configurations are computed analytically in the incipient post-buckling regime. Of particular interest is the variation of the first mode frequency as the load is increased through the buckling threshold. The loading type is found to have a crucial importance as the first mode frequency is shown to behave singularly in the zero thickness limit in the case of prescribed axial displacement, whereas a regular behavior is found in the case of prescribed axial load.This publication is based in part upon work supported by Award no. KUK-C1-013-04, made by King Abdullah University of Science and Technology (KAUST) (A.G.). A.G. is a Wolfson/Royal Society Merit Award holder. Support from the Royal Society, through the International Exchanges Scheme (Grant IE120203), is also acknowledge

Statistical Mechanics of Steiner trees

The Minimum Weight Steiner Tree (MST) is an important combinatorial optimization problem over networks that has applications in a wide range of fields. Here we discuss a general technique to translate the imposed global connectivity constrain into many local ones that can be analyzed with cavity equation techniques. This approach leads to a new optimization algorithm for MST and allows to analyze the statistical mechanics properties of MST on random graphs of various types

Exact asymptotics of the freezing transition of a logarithmically correlated random energy model

We consider a logarithmically correlated random energy model, namely a model for directed polymers on a Cayley tree, which was introduced by Derrida and Spohn. We prove asymptotic properties of a generating function of the partition function of the model by studying a discrete time analogy of the KPP-equation - thus translating Bramson's work on the KPP-equation into a discrete time case. We also discuss connections to extreme value statistics of a branching random walk and a rescaled multiplicative cascade measure beyond the critical point

Slowdown for time inhomogeneous branching Brownian motion

We consider the maximal displacement of one dimensional branching Brownian motion with (macroscopically) time varying profiles. For monotone decreasing variances, we show that the correction from linear displacement is not logarithmic but rather proportional to $T^{1/3}$. We conjecture that this is the worse case correction possible

Control of tumor and microenvironment cross-talk by miR-15a and miR-16 in prostate cancer

The interaction between cancer cells and microenvironment has a critical role in tumor development and progression. Although microRNAs regulate all the major biological mechanisms, their influence on tumor microenvironment is largely unexplored. Here, we investigate the role of microRNAs in the tumor-supportive capacity of stromal cells. We demonstrated that miR-15 and miR-16 are downregulated in fibroblasts surrounding the prostate tumors of the majority of 23 patients analyzed. Such downregulation of miR-15 and miR-16 in cancer-associated fibroblasts (CAFs) promoted tumor growth and progression through the reduced post-transcriptional repression of Fgf-2 and its receptor Fgfr1, which act on both stromal and tumor cells to enhance cancer cell survival, proliferation and migration. Moreover, reconstitution of miR-15 and miR-16 impaired considerably the tumor-supportive capability of stromal cells in vitro and in vivo. Our data suggest a molecular circuitry in which miR-15 and miR-16 and their correlated targets cooperate to promote tumor expansion and invasiveness through the concurrent activity on stromal and cancer cells, thus providing further support to the development of therapies aimed at reconstituting miR-15 and miR-16 in advanced prostate cancer. © 2011 Macmillan Publishers Limited All rights reserved

C-Met/miR-130b axis as novel mechanism and biomarker for castration resistance state acquisition

Although a significant subset of prostate tumors remain indolent during the entire life, the advanced forms are still one of the leading cause of cancer-related death. There are not reliable markers distinguishing indolent from aggressive forms. Here we highlighted a new molecular circuitry involving microRNA and coding genes promoting cancer progression and castration resistance. Our preclinical and clinical data demonstrated that c-Met activation increases miR-130b levels, inhibits androgen receptor expression, promotes cancer spreading and resistance to hormone ablation therapy. The relevance of these findings was confirmed on patients' samples and by in silico analysis on an independent patient cohort from Taylor's platform. Data suggest c-Met/miR-130b axis as a new prognostic marker for patients' risk assessment and as an indicator of therapy resistance. Our results propose new biomarkers for therapy decision-making in all phases of the pathology. Data may help identify high-risk patients to be treated with adjuvant therapy together with alternative cure for castration-resistant forms while facilitating the identification of possible patients candidates for anti-Met therapy. In addition, we demonstrated that it is possible to evaluate Met/miR-130b axis expression in exosomes isolated from peripheral blood of surgery candidates and advanced patients offering a new non-invasive tool for active surveillance and therapy monitoring

Diagnostic and prognostic potential of the proteomic profiling of serum-derived extracellular vesicles in prostate cancer

Extracellular vesicles (EVs) and their cargo represent an intriguing source of cancer biomarkers for developing robust and sensitive molecular tests by liquid biopsy. Prostate cancer (PCa) is still one of the most frequent and deadly tumor in men and analysis of EVs from biological fluids of PCa patients has proven the feasibility and the unprecedented potential of such an approach. Here, we exploited an antibody-based proteomic technology, i.e. the Reverse-Phase Protein microArrays (RPPA), to measure key antigens and activated signaling in EVs isolated from sera of PCa patients. Notably, we found tumor-specific protein profiles associated with clinical settings as well as candidate markers for EV-based tumor diagnosis. Among others, PD-L1, ERG, Integrin-β5, Survivin, TGF-β, phosphorylated-TSC2 as well as partners of the MAP-kinase and mTOR pathways emerged as differentially expressed endpoints in tumor-derived EVs. In addition, the retrospective analysis of EVs from a 15-year follow-up cohort generated a protein signature with prognostic significance. Our results confirm that serum-derived EV cargo may be exploited to improve the current diagnostic procedures while providing potential prognostic and predictive information. The approach proposed here has been already applied to tumor entities other than PCa, thus proving its value in translational medicine and paving the way to innovative, clinically meaningful tools