Minimal H\"older regularity implying finiteness of integral Menger curvature

We study two families of integral functionals indexed by a real number $p > 0$. One family is defined for 1-dimensional curves in $\R^3$ and the other one is defined for $m$-dimensional manifolds in $\R^n$. These functionals are described as integrals of appropriate integrands (strongly related to the Menger curvature) raised to power $p$. Given $p > m(m+1)$ we prove that $C^{1,\alpha}$ regularity of the set (a curve or a manifold), with $\alpha > \alpha_0 = 1 - \frac{m(m+1)}p$ implies finiteness of both curvature functionals ($m=1$ in the case of curves). We also show that $\alpha_0$ is optimal by constructing examples of $C^{1,\alpha_0}$ functions with graphs of infinite integral curvature

Latent Space Model for Multi-Modal Social Data

With the emergence of social networking services, researchers enjoy the increasing availability of large-scale heterogenous datasets capturing online user interactions and behaviors. Traditional analysis of techno-social systems data has focused mainly on describing either the dynamics of social interactions, or the attributes and behaviors of the users. However, overwhelming empirical evidence suggests that the two dimensions affect one another, and therefore they should be jointly modeled and analyzed in a multi-modal framework. The benefits of such an approach include the ability to build better predictive models, leveraging social network information as well as user behavioral signals. To this purpose, here we propose the Constrained Latent Space Model (CLSM), a generalized framework that combines Mixed Membership Stochastic Blockmodels (MMSB) and Latent Dirichlet Allocation (LDA) incorporating a constraint that forces the latent space to concurrently describe the multiple data modalities. We derive an efficient inference algorithm based on Variational Expectation Maximization that has a computational cost linear in the size of the network, thus making it feasible to analyze massive social datasets. We validate the proposed framework on two problems: prediction of social interactions from user attributes and behaviors, and behavior prediction exploiting network information. We perform experiments with a variety of multi-modal social systems, spanning location-based social networks (Gowalla), social media services (Instagram, Orkut), e-commerce and review sites (Amazon, Ciao), and finally citation networks (Cora). The results indicate significant improvement in prediction accuracy over state of the art methods, and demonstrate the flexibility of the proposed approach for addressing a variety of different learning problems commonly occurring with multi-modal social data.Comment: 12 pages, 7 figures, 2 table

Intelligent Self-Repairable Web Wrappers

The amount of information available on the Web grows at an incredible high rate. Systems and procedures devised to extract these data from Web sources already exist, and different approaches and techniques have been investigated during the last years. On the one hand, reliable solutions should provide robust algorithms of Web data mining which could automatically face possible malfunctioning or failures. On the other, in literature there is a lack of solutions about the maintenance of these systems. Procedures that extract Web data may be strictly interconnected with the structure of the data source itself; thus, malfunctioning or acquisition of corrupted data could be caused, for example, by structural modifications of data sources brought by their owners. Nowadays, verification of data integrity and maintenance are mostly manually managed, in order to ensure that these systems work correctly and reliably. In this paper we propose a novel approach to create procedures able to extract data from Web sources -- the so called Web wrappers -- which can face possible malfunctioning caused by modifications of the structure of the data source, and can automatically repair themselves.\u

Low prevalence, quasi-stationarity and power-law distribution in a model of spreading

Understanding how contagions (information, infections, etc) are spread on complex networks is important both from practical as well as theoretical point of view. Considerable work has been done in this regard in the past decade or so. However, most models are limited in their scope and as a result only capture general features of spreading phenomena. Here, we propose and study a model of spreading which takes into account the strength or quality of contagions as well as the local (probabilistic) dynamics occurring at various nodes. Transmission occurs only after the quality-based fitness of the contagion has been evaluated by the local agent. The model exhibits quality-dependent exponential time scales at early times leading to a slowly evolving quasi-stationary state. Low prevalence is seen for a wide range of contagion quality for arbitrary large networks. We also investigate the activity of nodes and find a power-law distribution with a robust exponent independent of network topology. Our results are consistent with recent empirical observations.Comment: 7 pages, 8 figures. (Submitted

Coronary artery endothelial dysfunction is positively correlated with low density lipoprotein and inversely correlated with high density lipoprotein subclass particles measured by nuclear magnetic resonance spectroscopy.

OBJECTIVE: The association between cholesterol and endothelial dysfunction remains controversial. We tested the hypothesis that lipoprotein subclasses are associated with coronary endothelial dysfunction. METHODS AND RESULTS: Coronary endothelial function was assessed in 490 patients between November 1993 and February 2007. Fasting lipids and nuclear magnetic resonance (NMR) lipoprotein particle subclasses were measured. There were 325 females and 165 males with a mean age of 49.8+/-11.6 years. Coronary endothelial dysfunction (epicardial constriction>20% or increase in coronary blood flow<50% in response to intracoronary acetylcholine) was diagnosed in 273 patients, the majority of whom (64.5%) had microvascular dysfunction. Total cholesterol and LDL-C (low density lipoprotein cholesterol) were not associated with endothelial dysfunction. One-way analysis and multivariate methods adjusting for age, gender, diabetes, hypertension and lipid-lowering agent use were used to determine the correlation between lipoprotein subclasses and coronary endothelial dysfunction. Epicardial endothelial dysfunction was significantly correlated with total (p=0.03) and small LDLp (LDL particles) (p<0.01) and inversely correlated with total and large HDLp (high density lipoprotein particles) (p<0.01). CONCLUSIONS: Epicardial, but not microvascular, coronary endothelial dysfunction was associated directly with LDL particles and inversely with HDL particles, suggesting location-dependent impact of lipoprotein particles on the coronary circulation

On Non-Abelian Symplectic Cutting

We discuss symplectic cutting for Hamiltonian actions of non-Abelian compact groups. By using a degeneration based on the Vinberg monoid we give, in good cases, a global quotient description of a surgery construction introduced by Woodward and Meinrenken, and show it can be interpreted in algebro-geometric terms. A key ingredient is the `universal cut' of the cotangent bundle of the group itself, which is identified with a moduli space of framed bundles on chains of projective lines recently introduced by the authors.Comment: Various edits made, to appear in Transformation Groups. 28 pages, 8 figure

A randomised controlled trial of a psychoeducational intervention for women at increased risk of breast cancer

This study aimed to compare the impact of two versions of a psychoeducational written intervention on cancer worry and objective knowledge of breast cancer risk-related topics in women who had been living with an increased risk of familial breast cancer for several years. Participants were randomised to three conditions: scientific and psychosocial information pack (Group 1), scientific information pack only (Group 2) or standard care control (Group 3). They completed postal questionnaires at baseline (n¼163) and\ud 4 weeks (n¼151). As predicted, there was a significant decrease in cancer worry for Group 1, but not Group 2. Objective\ud knowledge significantly improved for both Group 1 and Group 2 as expected, but not Group 3. However, there was an unpredicted\ud decline in cancer worry for Group 3. This study supports the value of a scientific and psychosocial information pack in providing up-to-date information related to familial risk of breast cancer for long-term attendees of a familial breast cancer clinic. Further research is warranted to determine how the information pack could be incorporated into the existing clinical service, thus providing these\ud women with the type of ongoing psychosocial support that many familial breast cancer clinics are currently lacking

High-Dimensional Menger-Type Curvatures-Part II: d-Separation and a Menagerie of Curvatures

This is the second of two papers wherein we estimate multiscale least squares approximations of certain measures by Menger-type curvatures. More specifically, we study an arbitrary d-regular measure on a real separable Hilbert space. The main result of the paper bounds the least squares error of approximation at any ball by an average of the discrete Menger-type curvature over certain simplices in in the ball. A consequent result bounds the Jones-type flatness by an integral of the discrete curvature over all simplices. The preceding paper provided the opposite inequalities. Furthermore, we demonstrate some other discrete curvatures for characterizing uniform rectifiability and additional continuous curvatures for characterizing special instances of the (p, q)-geometric property. We also show that a curvature suggested by Leger (Annals of Math, 149(3), p. 831-869, 1999) does not fit within our framework.Comment: 32 pages, no figure

Dynamic light scattering study on phase separation of a protein-water mixture: Application on cold cataract development in the ocular lens

We present a detailed dynamic light scattering study on the phase separation in the ocular lens emerging during cold cataract development. Cold cataract is a phase separation effect that proceeds via spinodal decomposition of the lens cytoplasm with cooling. Intensity auto-correlation functions of the lens protein content are analyzed with the aid of two methods providing information on the populations and dynamics of the scattering elements associated with cold cataract. It is found that the temperature dependence of many measurable parameters changes appreciably at the characteristic temperature ~16+1 oC which is associated with the onset of cold cataract. Extending the temperature range of this work to previously inaccessible regimes, i.e. well below the phase separation or coexistence curve at Tcc, we have been able to accurately determine the temperature dependence of the collective and self-diffusion coefficient of proteins near the spinodal. The analysis showed that the dynamics of proteins bears some resemblance to the dynamics of structural glasses where the apparent activation energy for particle diffusion increases below Tcc indicating a highly cooperative motion. Application of ideas developed for studying the critical dynamics of binary protein/solvent mixtures, as well as the use of a modified Arrhenius equation, enabled us to estimate the spinodal temperature Tsp of the lens nucleus. The applicability of dynamic light scattering as a non-invasive, early-diagnostic tool for ocular diseases is also demonstrated in the light of the findings of the present paper

Semitoric integrable systems on symplectic 4-manifolds

Let M be a symplectic 4-manifold. A semitoric integrable system on M is a pair of real-valued smooth functions J, H on M for which J generates a Hamiltonian S^1-action and the Poisson brackets {J,H} vanish. We shall introduce new global symplectic invariants for these systems; some of these invariants encode topological or geometric aspects, while others encode analytical information about the singularities and how they stand with respect to the system. Our goal is to prove that a semitoric system is completely determined by the invariants we introduce