Harold Jeffreys's Theory of Probability Revisited

Published exactly seventy years ago, Jeffreys's Theory of Probability (1939) has had a unique impact on the Bayesian community and is now considered to be one of the main classics in Bayesian Statistics as well as the initiator of the objective Bayes school. In particular, its advances on the derivation of noninformative priors as well as on the scaling of Bayes factors have had a lasting impact on the field. However, the book reflects the characteristics of the time, especially in terms of mathematical rigor. In this paper we point out the fundamental aspects of this reference work, especially the thorough coverage of testing problems and the construction of both estimation and testing noninformative priors based on functional divergences. Our major aim here is to help modern readers in navigating in this difficult text and in concentrating on passages that are still relevant today.Comment: This paper commented in: [arXiv:1001.2967], [arXiv:1001.2968], [arXiv:1001.2970], [arXiv:1001.2975], [arXiv:1001.2985], [arXiv:1001.3073]. Rejoinder in [arXiv:0909.1008]. Published in at http://dx.doi.org/10.1214/09-STS284 the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

Polarization forces in water deduced from single molecule data

Intermolecular polarization interactions in water are determined using a minimal atomic multipole model constructed with distributed polarizabilities. Hydrogen bonding and other properties of water-water interactions are reproduced to fine detail by only three multipoles $\mu_H$, $\mu_O$, and $\theta_O$ and two polarizabilities $\alpha_O$ and $\alpha_H$, which characterize a single water molecule and are deduced from single molecule data.Comment: 4 revtex pages, 3 embedded color PS figure

Truncated long-range percolation on oriented graphs

We consider different problems within the general theme of long-range percolation on oriented graphs. Our aim is to settle the so-called truncation question, described as follows. We are given probabilities that certain long-range oriented bonds are open; assuming that the sum of these probabilities is infinite, we ask if the probability of percolation is positive when we truncate the graph, disallowing bonds of range above a possibly large but finite threshold. We give some conditions in which the answer is affirmative. We also translate some of our results on oriented percolation to the context of a long-range contact process.Comment: 9 pages, 1 figur

Finding Exogenous Variables in Data with Many More Variables than Observations

Many statistical methods have been proposed to estimate causal models in classical situations with fewer variables than observations (p<n, p: the number of variables and n: the number of observations). However, modern datasets including gene expression data need high-dimensional causal modeling in challenging situations with orders of magnitude more variables than observations (p>>n). In this paper, we propose a method to find exogenous variables in a linear non-Gaussian causal model, which requires much smaller sample sizes than conventional methods and works even when p>>n. The key idea is to identify which variables are exogenous based on non-Gaussianity instead of estimating the entire structure of the model. Exogenous variables work as triggers that activate a causal chain in the model, and their identification leads to more efficient experimental designs and better understanding of the causal mechanism. We present experiments with artificial data and real-world gene expression data to evaluate the method.Comment: A revised version of this was published in Proc. ICANN201

Unsteady Simulation of CO/H2/N2/air Turbulent Non-Premixed Flame

The Sandia/ETH-Zurich CO/H2/N2 non-premixed unconfined turbulent jet flame (named ‘Flame A’) is numerically simulated by solving the unsteady compressible reactive Navier– Stokes equations in a three-dimensional axisymmetric formulation, hence, in a formally twodimensional domain. The turbulent combustion closure model adopted is the Fractal Model, FM, developed as a subgrid scale model for Large Eddy Simulation. The fuel is injected from a straight circular tube and the corresponding Reynolds number is 16 700, while the air coflows. Since the thickness of the nozzle is 0.88 mm, and the injection velocity high, ?104ms?1, capturing the stabilization mechanism of the actual flame requires high spatial resolution close to the injector. Results are first obtained on a coarse grid assuming a fast-chemistry approach for hydrogen oxidation and a single step mechanism for carbon monoxide oxidation.With this approach the flame is inevitably anchored. Then, to understand the actual flame stabilization a more complex chemical mechanism, including main radical species, is adopted. Since using this chemistry and the coarse grid of previous simulation the flame blows off numerically, attention is focused on understanding the actual flame stabilization mechanism by simulating a small spatial region close to the injection with a very fine grid. Then, analysing these results, an artificial anchoring mechanism is developed to be used in simulations of the whole flame with a coarse grid. Unsteady characteristics are shown and some averaged radial profiles for temperature and species are compared with experimental data

Timely Supplementation of Hydrogels Containing Sulfated or Unsulfated Chondroitin and Hyaluronic Acid Affects Mesenchymal Stromal Cells Commitment Toward Chondrogenic Differentiation

Mesenchymal stromal cells (MSCs) are currently used for cartilage cell therapy because of their well proven capacity to differentiate in chondrocytes. The advantage of MSC-based therapy is the possibility of producing a high number of chondrocytes for implants. The transplant procedure, however, has some limitations, since MSCs may produce non-functional chondrocytes. This limit has been challenged by cultivating MSC in media with hydrogels containing hyaluronic acid (HA), extractive chondroitin sulfate (CS), or bio-fermentative unsulphated chondroitin (BC) alone or in combination. Nevertheless, a clear study of the effect of glycosaminoglycans (GAGs) on chondrocyte differentiation is still lacking, especially for the newly obtained unsulfated chondroitin of biotechnological origin. Are these GAGs playing a role in the commitment of stem cells to chondrocyte progenitors and in the differentiation of progenitors to mature chondrocytes? Alternatively, do they have a role only in one of these biological processes? We evaluated the role of HA, CS, and – above all – BC in cell commitment and chondrocyte differentiation of MSCs by supplementing these GAGs in different phases of in vitro cultivation. Our data provided evidence that a combination of HA and CS or of HA and BC supplemented during the terminal in vitro differentiation and not during cell commitment of MSCs improved chondrocytes differentiation without the presence of fibrosis (reduced expression of Type I collagen). This result suggests that a careful evaluation of extracellular cues for chondrocyte differentiation is fundamental to obtaining a proper maturation process

Geometry of the energy landscape of the self-gravitating ring

We study the global geometry of the energy landscape of a simple model of a self-gravitating system, the self-gravitating ring (SGR). This is done by endowing the configuration space with a metric such that the dynamical trajectories are identified with geodesics. The average curvature and curvature fluctuations of the energy landscape are computed by means of Monte Carlo simulations and, when possible, of a mean-field method, showing that these global geometric quantities provide a clear geometric characterization of the collapse phase transition occurring in the SGR as the transition from a flat landscape at high energies to a landscape with mainly positive but fluctuating curvature in the collapsed phase. Moreover, curvature fluctuations show a maximum in correspondence with the energy of a possible further transition, occurring at lower energies than the collapse one, whose existence had been previously conjectured on the basis of a local analysis of the energy landscape and whose effect on the usual thermodynamic quantities, if any, is extremely weak. We also estimate the largest Lyapunov exponent $\lambda$ of the SGR using the geometric observables. The geometric estimate always gives the correct order of magnitude of $\lambda$ and is also quantitatively correct at small energy densities and, in the limit $N\to\infty$, in the whole homogeneous phase.Comment: 20 pages, 12 figure

Muse stem cells can be isolated from stromal compartment of mouse bone marrow, adipose tissue, and ear connective tissue: A comparative study of their in vitro properties

The cells present in the stromal compartment of many tissues are a heterogeneous population containing stem cells, progenitor cells, fibroblasts, and other stromal cells. A SSEA3(+) cell subpopulation isolated from human stromal compartments showed stem cell properties. These cells, known as multilineage-differentiating stress-enduring (MUSE) cells, are capable of resisting stress and possess an excellent ability to repair DNA damage. We isolated MUSE cells from different mouse stromal compartments, such as those present in bone marrow, subcutaneous white adipose tissue, and ear connective tissue. These cells showed overlapping in vitro biological properties. The mouse MUSE cells were positive for stemness markers such as SOX2, OCT3/4, and NANOG. They also expressed TERT, the catalytic telomerase subunit. The mouse MUSE cells showed spontaneous commitment to differentiation in meso/ecto/endodermal derivatives. The demonstration that mul-tilineage stem cells can be isolated from an animal model, such as the mouse, could offer a valid alternative to the use of other stem cells for disease studies and envisage of cellular therapies