Constant density visualizations of non-uniform distributions of data

1998 ◽  
Author(s):  
Allison Woodruff ◽  
James Landay ◽  
Michael Stonebraker
Keyword(s):  
Constant Density ◽  
Uniform Distributions

Pressure variation in a fluid at rest (hydrostatics)

2018 ◽  
Author(s):  
Marcel Escudier
Keyword(s):  
Equation Of State ◽  
Static Pressure ◽  
Applied Pressure ◽  
Pressure Variation ◽  
Constant Density ◽  
Fluid Temperature ◽  
Earth’S Atmosphere ◽  
Hydrostatic Equation ◽  
Depth Increase ◽  
Pressure Changes

The three fundamental principles for the variation of static pressure p throughout a body of fluid at rest are (a) the pressure at a point is the same in all directions (Pascal’s law), (b) the pressure is the same at all points on the same horizontal level, and (c) the pressure increases with depth z according to the hydrostatic equation. dp/dz= ρ‎g For a fluid with constant density ρ‎, the increase in pressure over a depth increase h is ρ‎gh, a result which can be used to analyse the response of simple barometers and manometers to applied pressure changes and differences. In situations where very large changes in pressure occur an equation of state may be required to relate pressure and density together with an assumption about the fluid temperature. The hydrostatic equation is still valid but more difficult to integrate, as illustrated by consideration of the earth’s atmosphere.

An Introduction to Statistical Models for Networks

2020 ◽  
pp. 218-233
Author(s):  
Valentina Kuskova ◽  
Stanley Wasserman
Keyword(s):  
Social System ◽  
Exponential Family ◽  
Behavioral Science ◽  
Social Science Research ◽  
Science Research ◽  
Uniform Distributions ◽  
The Social ◽  
Special Cases ◽  
Social And Behavioral Science ◽  
Network Methods

Network theoretical and analytic approaches have reached a new level of sophistication in this decade, accompanied by a rapid growth of interest in adopting these approaches in social science research generally. Of course, much social and behavioral science focuses on individuals, but there are often situations where the social environment—the social system—affects individual responses. In these circumstances, to treat individuals as isolated social atoms, a necessary assumption for the application of standard statistical analysis is simply incorrect. Network methods should be part of the theoretical and analytic arsenal available to sociologists. Our focus here will be on the exponential family of random graph distributions, p*, because of its inclusiveness. It includes conditional uniform distributions as special cases.

scholarly journals Swarm Learning for decentralized and confidential clinical machine learning

Nature ◽  
2021 ◽  
Author(s):  
Stefanie Warnat-Herresthal ◽  
◽  
Hartmut Schultze ◽  
Krishnaprasad Lingadahalli Shastry ◽  
Sathyanarayanan Manamohan ◽  
...  
Keyword(s):  
Machine Learning ◽  
Precision Medicine ◽  
Distributed Data ◽  
X Ray ◽  
Uniform Distributions ◽  
Privacy Laws ◽  
Data Owner ◽  
Machine Learning Approach ◽  
Chest X Ray ◽  
Privacy Legislation

AbstractFast and reliable detection of patients with severe and heterogeneous illnesses is a major goal of precision medicine1,2. Patients with leukaemia can be identified using machine learning on the basis of their blood transcriptomes3. However, there is an increasing divide between what is technically possible and what is allowed, because of privacy legislation4,5. Here, to facilitate the integration of any medical data from any data owner worldwide without violating privacy laws, we introduce Swarm Learning—a decentralized machine-learning approach that unites edge computing, blockchain-based peer-to-peer networking and coordination while maintaining confidentiality without the need for a central coordinator, thereby going beyond federated learning. To illustrate the feasibility of using Swarm Learning to develop disease classifiers using distributed data, we chose four use cases of heterogeneous diseases (COVID-19, tuberculosis, leukaemia and lung pathologies). With more than 16,400 blood transcriptomes derived from 127 clinical studies with non-uniform distributions of cases and controls and substantial study biases, as well as more than 95,000 chest X-ray images, we show that Swarm Learning classifiers outperform those developed at individual sites. In addition, Swarm Learning completely fulfils local confidentiality regulations by design. We believe that this approach will notably accelerate the introduction of precision medicine.

scholarly journals Recursive algorithms for the computation of the potential harmonic coefficients of a constant density polyhedron

2009 ◽  
Vol 83 (10) ◽  
pp. 925-942 ◽  
Author(s):  
Dimitrios Tsoulis ◽  
Olivier Jamet ◽  
Jérôme Verdun ◽  
Nicolas Gonindard
Keyword(s):  
Constant Density ◽  
Recursive Algorithms ◽  
Potential Harmonic

scholarly journals Distributions associated with simultaneous multiple hypothesis testing

2020 ◽  
Vol 7 (1) ◽  
Author(s):  
Chang Yu ◽  
Daniel Zelterman
Keyword(s):  
Latent Variable ◽  
Power Analysis ◽  
Marginal Distribution ◽  
Multiple Hypothesis Testing ◽  
Family Wise Error Rate ◽  
Uniform Distributions ◽  
Multiple Hypothesis ◽  
The Family ◽  
Alternative Hypotheses ◽  
Cancer Studies

Abstract We develop the distribution for the number of hypotheses found to be statistically significant using the rule from Simes (Biometrika 73: 751–754, 1986) for controlling the family-wise error rate (FWER). We find the distribution of the number of statistically significant p-values under the null hypothesis and show this follows a normal distribution under the alternative. We propose a parametric distribution ΨI(·) to model the marginal distribution of p-values sampled from a mixture of null uniform and non-uniform distributions under different alternative hypotheses. The ΨI distribution is useful when there are many different alternative hypotheses and these are not individually well understood. We fit ΨI to data from three cancer studies and use it to illustrate the distribution of the number of notable hypotheses observed in these examples. We model dependence in sampled p-values using a latent variable. These methods can be combined to illustrate a power analysis in planning a larger study on the basis of a smaller pilot experiment.

scholarly journals Stabilizing effect of methylcellulose on the dispersion of multi-walled carbon nanotubes in cementitious composites

2020 ◽  
Vol 9 (1) ◽  
pp. 93-104
Author(s):  
Mingrui Du ◽  
Yuan Gao ◽  
Guansheng Han ◽  
Luan Li ◽  
Hongwen Jing
Keyword(s):  
Carbon Nanotubes ◽  
Pore Solution ◽  
Cementitious Materials ◽  
High Ionic Strength ◽  
Cementitious Composites ◽  
Uniform Distributions ◽  
Stabilizing Effect ◽  
Multi Walled Carbon Nanotubes ◽  
The Stability ◽  
Walled Carbon Nanotubes

AbstractMulti-walled carbon nanotubes (MWCNTs) have been added in the plain cementitious materials to manufacture composites with the higher mechanical properties and smart behavior. The uniform distributions of MWCNTs is critical to obtain the desired enhancing effect, which, however, is challenged by the high ionic strength of the cement pore solution. Here, the effects of methylcellulose (MC) on stabilizing the dispersion of MWCNTs in the simulated cement pore solution and the viscosity of MWCNT suspensions werestudied. Further observations on the distributions of MWCNTs in the ternary cementitious composites were conducted. The results showed that MC forms a membranous envelope surrounding MWCNTs, which inhibits the adsorption of cations and maintains the steric repulsion between MWCNTs; thus, the stability of MWCNT dispersion in cement-based composites is improved. MC can also work as a viscosity adjuster that retards the Brownian mobility of MWCNTs, reducing their re-agglomerate within a period. MC with an addition ratio of 0.018 wt.% is suggested to achieve the optimum dispersion stabilizing effect. The findings here provide a way for stabilizing the other dispersed nano-additives in the cementitious composites.

Laminar natural convection about an isothermally heated sphere at small Grashof number

1968 ◽  
Vol 34 (1) ◽  
pp. 163-176 ◽  
Author(s):  
Francis E. Fendell
Keyword(s):  
Natural Convection ◽  
Three Dimensional ◽  
Perturbation Expansion ◽  
Outer Sphere ◽  
Convective Transport ◽  
Convection Flow ◽  
Constant Density ◽  
Boussinesq Model ◽  
Grashof Number ◽  
Recirculating Flow

The flow induced by gravity about a very small heated isothermal sphere introduced into a fluid in hydrostatic equilibrium is studied. The natural-convection flow is taken to be steady and laminar. The conditions under which the Boussinesq model is a good approximation to the full conservation laws are described. For a concentric finite cold outer sphere with radius, in ratio to the heated sphere radius, roughly less than the Grashof number to the minus one-half power, a recirculating flow occurs; fluid rises near the inner sphere and falls near the outer sphere. For a small heated sphere in an unbounded medium an ordinary perturbation expansion essentially in the Grashof number leads to unbounded velocities far from the sphere; this singularity is the natural-convection analogue of the Whitehead paradox arising in three-dimensional low-Reynolds-number forced-convection flows. Inner-and-outer matched asymptotic expansions reveal the importance of convective transport away from the sphere, although diffusive transport is dominant near the sphere. Approximate solution is given to the nonlinear outer equations, first by seeking a similarity solution (in paraboloidal co-ordinates) for a point heat source valid far from the point source, and then by linearization in the manner of Oseen. The Oseen solution is matched to the inner diffusive solution. Both outer solutions describe a paraboloidal wake above the sphere within which the enthalpy decays slowly relative to the rapid decay outside the wake. The updraft above the sphere is reduced from unbounded growth with distance from the sphere to constant magnitude by restoration of the convective accelerations. Finally, the role of vertical stratification of the ambient density in eventually stagnating updrafts predicted on the basis of a constant-density atmosphere is discussed.

A static generalization of the Einstein universe

1958 ◽  
Vol 245 (1241) ◽  
pp. 202-212
Keyword(s):  
General Problem ◽  
Constant Density ◽  
De Sitter ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Einstein Universe

Solutions of the Einstein field equations are found for the problem of a sphere of constant density surrounded by matter of different constant density. The solutions are discussed and particular attention paid to the topology of the surrounding matter. The Schwarzschild, de Sitter, and Einstein solutions emerge as particular cases of the general problem.

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