The difference between advancing and receding contact angles is termed contact angle hysteresis and can be used to characterize surface heterogeneity, roughness, and mobility. Surfaces that are not homogeneous will have domains that impede motion of the contact line. The slide angle is another dynamic measure of hydrophobicity and is measured by depositing a droplet on a surface and tilting the surface until the droplet begins to slide. In general, liquids in the Cassie–Baxter state exhibit lower slide angles and contact angle hysteresis than those in the Wenzel state.
omitted variable biasomitted variablesomitted variable
In statistics, omitted-variable bias (OVB) occurs when a statistical model leaves out one or more relevant variables. The bias results in the model attributing the effect of the missing variables to the estimated effects of the included variables.
Octane is a hydrocarbon and an alkane with the chemical formula C 8 H 18, and the condensed structural formula CH 3 (CH 2 ) 6 CH 3. Octane has many structural isomers that differ by the amount and location of branching in the carbon chain. One of these isomers, 2,2,4-trimethylpentane (isooctane) is used as one of the standard values in the octane rating scale.
Errors-in-variables modelerrors-in-variableserrors in variables
However there are several techniques which make use of some additional data: either the instrumental variables, or repeated observations. In this approach two (or maybe more) repeated observations of the regressor x* are available. Both observations contain their own measurement errors, however those errors are required to be independent: : where x* ⊥ η 1 ⊥ η 2. Variables η 1, η 2 need not be identically distributed (although if they are efficiency of the estimator can be slightly improved).
Silicone grease, sometimes called dielectric grease, is a waterproof grease made by combining a silicone oil with a thickener. Most commonly, the silicone oil is polydimethylsiloxane (PDMS) and the thickener is amorphous fumed silica. Using this formulation, silicone grease is a translucent white viscous paste, with exact properties dependent on the type and proportion of the components. More specialized silicone greases are made from fluorinated silicones or, for low-temperature applications, PDMS containing some phenyl substituents in place of methyl groups. Other thickeners may be used, including stearates and powdered polytetrafluorethylene (PTFE).
Diffusion of reagents on the surface of a catalyst may play an important role in heterogeneous catalysis. The model of diffusion in the ideal monolayer is based on the jumps of the reagents on the nearest free places. This model was used for CO on Pt oxidation under low gas pressure. The system includes several reagents on the surface. Their surface concentrations are The surface is a lattice of the adsorption places. Each reagent molecule fills a place on the surface. Some of the places are free. The concentration of the free places is z=c_0. The sum of all c_i (including free places) is constant, the density of adsorption places b.
Robert Rosenthal (born March 2, 1933) is a German-born American psychologist who is a Distinguished Professor of Psychology at the University of California, Riverside. His interests include self-fulfilling prophecies, which he explored in a well-known study of the Pygmalion Effect: the effect of teachers' expectations on students.
It has been speculated, since the 19th century, that the universe is fated to a heat death in which all the energy ends up as a homogeneous distribution of thermal energy so that no more work can be extracted from any source. If the universe can be considered to have generally increasing entropy, then – as Roger Penrose has pointed out – gravity plays an important role in the increase because gravity causes dispersed matter to accumulate into stars, which collapse eventually into black holes. The entropy of a black hole is proportional to the surface area of the black hole's event horizon.
sampling variabilitysampling variationless reliable
In statistics, sampling errors are incurred when the statistical characteristics of a population are estimated from a subset, or sample, of that population. Since the sample does not include all members of the population, statistics on the sample, such as means and quartiles, generally differ from the characteristics of the entire population, which are known as parameters. For example, if one measures the height of a thousand individuals from a country of one million, the average height of the thousand is typically not the same as the average height of all one million people in the country.
simultaneous equationssystems of equationssimultaneous equation
In mathematics, a set of simultaneous equations, also known as a system of equations or an equation system, is a finite set of equations for which common solutions are sought. An equation system is usually classified in the same manner as single equations, namely as a:
A chemical compound is a chemical substance composed of many identical molecules (or molecular entities) composed of atoms from more than one element held together by chemical bonds. Two atoms of the same element bonded in a molecule do not form a chemical compound, since this would require two different elements.
Frisch–Waugh theoremFWL theorempartialed out
In econometrics, the Frisch–Waugh–Lovell (FWL) theorem is named after the econometricians Ragnar Frisch, Frederick V. Waugh, and Michael C. Lovell.
"Gorp" redirects here. For other uses, see Gorp (disambiguation). "Scroggin" redirects here. It is not to be confused with.
Bayesian networkshierarchical Bayes modelhierarchical Bayesian model
A hierarchical Bayes Model for handling sample heterogeneity in classification problems, provides a classification model taking into consideration the uncertainty associated with measuring replicate samples. Hierarchical Naive Bayes Model for handling sample uncertainty, shows how to perform classification and learning with continuous and discrete variables with replicated measurements.
Heterogeneous catalysts are usually solids, powdered in order to maximize their surface area. Of particular importance in heterogeneous catalysis are the platinum group metals and other transition metals, which are used in hydrogenations, catalytic reforming and in the synthesis of commodity chemicals such as nitric acid and ammonia. Acids are an example of a homogeneous catalyst, they increase the nucleophilicity of carbonyls, allowing a reaction that would not otherwise proceed with electrophiles. The advantage of homogeneous catalysts is the ease of mixing them with the reactants, but they may also be difficult to separate from the products.
modelprobabilistic modelstatistical modeling
A statistical model is a mathematical model that embodies a set of statistical assumptions concerning the generation of sample data (and similar data from a larger population). A statistical model represents, often in considerably idealized form, the data-generating process.
MCMCMarkov chain Monte Carlo (MCMC)Bayesian MCMC
In statistics, Markov chain Monte Carlo (MCMC) methods comprise a class of algorithms for sampling from a probability distribution. By constructing a Markov chain that has the desired distribution as its equilibrium distribution, one can obtain a sample of the desired distribution by recording states from the chain. The more steps that are included, the more closely the distribution of the sample matches the actual desired distribution. Various algorithms exist for constructing the Markov chain including the Metropolis–Hastings algorithm.
In the physical sciences, a phase is a region of space (a thermodynamic system), throughout which all physical properties of a material are essentially uniform. Examples of physical properties include density, index of refraction, magnetization and chemical composition. A simple description is that a phase is a region of material that is chemically uniform, physically distinct, and (often) mechanically separable. In a system consisting of ice and water in a glass jar, the ice cubes are one phase, the water is a second phase, and the humid air is a third phase over the ice and water. The glass of the jar is another separate phase. (See )
A receiver operating characteristic curve, or ROC curve, is a graphical plot that illustrates the diagnostic ability of a binary classifier system as its discrimination threshold is varied.
Alan B. KruegerKruegerDr. Alan Krueger
Alan Bennett Krueger (September 17, 1960 – March 16, 2019) was an American economist who was the James Madison Professor of Political Economy at Princeton University and Research Associate at the National Bureau of Economic Research. He served as Assistant Secretary of the Treasury for Economic Policy, nominated by President Barack Obama, from May 2009 to October 2010, when he returned to Princeton. He was nominated in 2011 by Obama as chair of the White House Council of Economic Advisers, and served in that office from November 2011 to August 2013. He was among the 50 highest ranked economists in the world according to Research Papers in Economics.
A reagent is a substance or compound added to a system to cause a chemical reaction, or added to test if a reaction occurs. The terms reactant and reagent are often used interchangeably—however, a reactant is more specifically a substance consumed in the course of a chemical reaction. Solvents, though involved in the reaction, are usually not called reactants. Similarly, catalysts are not consumed by the reaction, so they are not reactants. In biochemistry, especially in connection with enzyme-catalyzed reactions, the reactants are commonly called substrates.
cross-validationcross validationLeave-one-out cross-validation
A recent development in medical statistics is its use in meta-analysis. It forms the basis of the validation statistic, Vn which is used to test the statistical validity of meta-analysis summary estimates. It has also been used in a more conventional sense in meta-analysis to estimate the likely prediction error of meta-analysis results. By performing an initial analysis to identify the most informative features using the entire data set – if feature selection or model tuning is required by the modeling procedure, this must be repeated on every training set. Otherwise, predictions will certainly be upwardly biased.
In statistics, econometrics, epidemiology, genetics and related disciplines, causal graphs (also known as path diagrams, causal Bayesian networks or DAGs) are probabilistic graphical models used to encode assumptions about the data-generating process. They can also be viewed as a blueprint of the algorithm by which Nature assigns values to the variables in the domain of interest.
negative resultsnull resultsnegative
In science, a null result is a result without the expected content: that is, the proposed result is absent. It is an experimental outcome which does not show an otherwise expected effect. This does not imply a result of zero or nothing, simply a result that does not support the hypothesis.
statistically significantsignificantsignificance level
In statistical hypothesis testing, a result has statistical significance when it is very unlikely to have occurred given the null hypothesis. More precisely, a study's defined significance level, denoted by \alpha, is the probability of the study rejecting the null hypothesis, given that the null hypothesis were assumed to be true; and the p-value of a result, p, is the probability of obtaining a result at least as extreme, given that the null hypothesis were true. The result is statistically significant, by the standards of the study, when . The significance level for a study is chosen before data collection, and is typically set to 5% or much lower—depending on the field of study.