Geometric Sobolev-like embedding using high-dimensional Menger-like curvature

We study a modified version of Lerman-Whitehouse Menger-like curvature defined for m+2 points in an n-dimensional Euclidean space. For 1 <= l <= m+2 and an m-dimensional subset S of R^n we also introduce global versions of this discrete curvature, by taking supremum with respect to m+2-l points on S. We then define geometric curvature energies by integrating one of the global Menger-like curvatures, raised to a certain power p, over all l-tuples of points on S. Next, we prove that if S is compact and m-Ahlfors regular and if p is greater than ml, then the P. Jones' \beta-numbers of S must decay as r^t with r \to 0 for some t in (0,1). If S is an immersed C^1 manifold or a bilipschitz image of such set then it follows that it is Reifenberg flat with vanishing constant, hence (by a theorem of David, Kenig and Toro) an embedded C^{1,t} manifold. We also define a wide class of other sets for which this assertion is true. After that, we bootstrap the exponent t to the optimal one a = 1 - ml/p showing an analogue of the Morrey-Sobolev embedding theorem. Moreover, we obtain a qualitative control over the local graph representations of S only in terms of the energy.Comment: I removed Example 3.11, which was wrong in the sense that the \beta-numbers for this set do not decay as r^

The Energetic Backpacks in BEC

What should the equipment for multifunctional building used simultaneously by thousands of people be like? Let’s start with the (architectural) logic: - Such a space must allow for people’s movement and carry out activity with total freedom, without the interference of the necessary and voluminous service shafts. - Services must be easily accessible for maintenance

Computational engine structural analysis

A significant research activity at the NASA Lewis Research Center is the computational simulation of complex multidisciplinary engine structural problems. This simulation is performed using computational engine structural analysis (CESA) which consists of integrated multidisciplinary computer codes in conjunction with computer post-processing for problem-specific application. A variety of the computational simulations of specific cases are described in some detail in this paper. These case studies include: (1) aeroelastic behavior of bladed rotors, (2) high velocity impact of fan blades, (3) blade-loss transient response, (4) rotor/stator/squeeze-film/bearing interaction, (5) blade-fragment/rotor-burst containment, and (6) structural behavior of advanced swept turboprops. These representative case studies are selected to demonstrate the breath of the problems analyzed and the role of the computer including post-processing and graphical display of voluminous output data

MODELLING THE INFLUENCE OF NUCLEUS ELASTICITY ON CELL INVASION IN FIBER NETWORKS AND MICROCHANNELS

Cell migration in highly constrained extracellular matrices is exploited in scaffold-based tissue engineering and is fundamental in a wide variety of physiological and pathological phenomena, among others in cancer invasion and development. Research into the critical processes involved in cell migration has mainly focused on cell adhesion and proteolytic degradation of the external environment. However, rising evidence has recently shown that a number of cell-derived biophysical and mechanical parameters, among others nucleus stiffness and cell deformability, plays a major role in cell motility, especially in the ameboid-like migration mode in 3D confined tissue structures. We here present an extended cellular Potts model (CPM) first used to simulate a micro-fabricated migration chip, which tests the active invasive behavior of cancer cells into narrow channels. As distinct features of our approach, cells are modeled as compartmentalized discrete objects, differentiated in the nucleus and in the cytosolic region, while the migration chamber is composed of channels of different widths. We find that cell motile phenotype and velocity in open spaces (i.e., 2D flat surfaces or large channels) are not significantly influenced by cell elastic properties. On the contrary, the migratory behavior of cells within subcellular and subnuclear structures strongly relies on the deformability of the cytosol and of the nuclear cluster, respectively. Further, we characterize two migration dynamics: a stepwise way, characterized by fluctuations in cell length, within channels smaller than nucleus dimensions and a smooth sliding (i.e., maintaining constant cell length) behavior within channels larger than the nuclear cluster. These resulting observations are then extended looking at cell migration in an artificial fiber network, which mimics cell invasion in a 3D extracellular matrix. In particular, in this case, we analyze the effect of variations in elasticity of the nucleus on cell movement. In order to summarize, with our simulated migration assays, we demonstrate that the dimensionality of the environment strongly affects the migration phenotype and we suggest that the cytoskeletal and nuclear elastic characteristics correlate with the tumor cell's invasive potentia

Life editing: Third-party perspectives on lifelog content

Lifelog collections digitally capture and preserve personal experiences and can be mined to reveal insights and understandings of individual significance. These rich data sources also offer opportunities for learning and discovery by motivated third parties. We employ a custom-designed storytelling application in constructing meaningful lifelog summaries from third-party perspectives. This storytelling initiative was implemented as a core component in a university media-editing course. We present promising results from a preliminary study conducted to evaluate the utility and potential of our approach in creatively interpreting a unique experiential dataset

Formation and Structure of Low Density Exo-Neptunes

Kepler has found hundreds of Neptune-size (2-6 R_Earth) planet candidates within 0.5 AU of their stars. The nature of the vast majority of these planets is not known because their masses have not been measured. Using theoretical models of planet formation, evolution and structure, we explore the range of minimum plausible masses for low-density exo-Neptunes. We focus on highly irradiated planets with T_eq>=500K. We consider two separate formation pathways for low-mass planets with voluminous atmospheres of light gases: core nucleated accretion and outgassing of hydrogen from dissociated ices. We show that Neptune-size planets at T_eq=500K with masses as small as a few times that of Earth can plausibly be formed core nucleated accretion coupled with subsequent inward migration. We also derive a limiting low-density mass-radius relation for rocky planets with outgassed hydrogen envelopes but no surface water. Rocky planets with outgassed hydrogen envelopes typically have computed radii well below 3 R_Earth. For both planets with H/He envelopes from core nucleated accretion and planets with outgassed hydrogen envelopes, we employ planet interior models to map the range of planet mass--envelope mass--equilibrium temperature parameter space that is consistent with Neptune-size planet radii. Atmospheric mass loss mediates which corners of this parameter space are populated by actual planets and ultimately governs the minimum plausible mass at a specified transit radius. We find that Kepler's 2-6 R_Earth planet candidates at T_eq=500--1000K could potentially have masses less than ~4 M_Earth. Although our quantitative results depend on several assumptions, our qualitative finding that warm Neptune-size planets can have masses substantially smaller than those given by interpolating the masses and radii of planets within our Solar System is robust.Comment: 17 pages, 9 figures, accepted for publication in Ap

Guidelines for the presentation and visualisation of lifelog content

Lifelogs offer rich voluminous sources of personal and social data for which visualisation is ideally suited to providing access, overview, and navigation. We explore through examples of our visualisation work within the domain of lifelogging the major axes on which lifelogs operate, and therefore, on which their visualisations should be contingent. We also explore the concept of ‘events’ as a way to significantly reduce the complexity of the lifelog for presentation and make it more human-oriented. Finally we present some guidelines and goals which should be considered when designing presentation modes for lifelog conten