Kusanthura-Maŵiro (kufuma ku ChiGerman: Statistik,  "kulongosora boma, la charu") ni kafukufuku uyo wakukhwaskana na kuwunjika, kwendeska, kusanda, kung'anamura, na kulongosora uthenga. Para tikugwiliskira ntchito Kusanthura-Maŵiro pa suzgo la sayansi, malonda, panji la umoyo wa ŵanthu, kanandi tikwamba na Unandi-wose panjiso kayezgero ka Kusanthura-Maŵiro ako katiŵazgikenge. Unandi-wose, ungaŵa vigaŵa vyakupambana pambana vya ŵanthu panji vinthu nga "ŵanthu ŵose ŵakukhala mu charu" panji "chimenyu chilichose chakuwumba khristoli". Kusanthura-Maŵiro kukuwona vyose vyakukhwaskana na umo vinthu viliri, kusazgapo ndondomeko ya kunozga ma Save na ma kafukufuku.

Pala uthenga wa chipendero ungatoleleka yayi, waKusanthura-Maŵiro wakutolela uthenga pakupanga makafukufuku na ma save ago ghakugwiliska ntchito viyezgero. Kutola viyezgero vyakwimilra yikuwoneseska kuti fundo zingatandazga mwa mahara kufuma ku kachiyezgero kuluta ku unandi-wose mwanthunthu. Kafukufuku wakusanda kukukhwaska kupima vinthu ivyo vikusangika mu ndondomeko iyo yikusambizgika, kunjizgapo vinthu vinyake ivyo vikusintha vinthu ivi, na kupima vinthu vinyake ivyo vikuchitika mwakuyana na ndondomeko iyo yikapangika kuti ŵanthu ŵamanye usange vinthu ivi vyasintha vinthu ivyo vikupima. Mwakupambaniska, kusanda Kwakulaŵilira kukukhwaska kafukufuku wakuseŵeleska yayi.

Vyakudanga viŵiri mwa nthowa za Kusanthura-Maŵiro yakugwiliskika mu kusanda uthenga: Kusanthura-Maŵiro kwakulongosoleka, Ivyo vikuyowoya mwakudumura ivyo vyafuma mu viyezgero kugwiriska maindekse nthe tikatikati panji yisezgo yakukhazikika, na Kusanthura-Maŵiro mwa fundo, izo zikufunya fundo kufuma pa uthenga uwo ukupambanangapambananga (nthe, vyakubekeka mwautesi, upambano wa viyezgero). Kusanthura-Maŵiro ghakulongosoleka kanandi ghakukhwaska magulu yaŵiri ya maunenesko gha chigaŵo (chiyezgero panji unandi-wose): uzgoloŵezgi wa pakati (pangi malo) uikukhumba kulongora umo vinthu viliri pakatikati panji umo vikuŵira, apo kusakatuka (panji kuti kusinthasintha) kukulongora umo ŵanthu ŵakufumira pakati pa vinthu. Fundo zakuroska mu Kusanthura-Maŵiro musamuzi zikupangika pa chizengero cha fundo ya mayero, iyi yikulongosora umo vinthu vikuchitikira mwamwaŵi.

Kanandi ndondomeko ya Kusanthura-Maŵiro kukukhwaska kutolela kwa uthenga kulazgiska ku kuyezga kwa ubali pakati pa vibwayila viŵiri vya Kusanthura-Maŵiro, panji vibwayila vyauthenga na mauthenga ghakuwumbika na ŵanthu kufuma ku chiyezgero chakuwumbika mwausuma. Chiloskero chikupelekeka kulongosola ubali wa Kusanthura-Maŵiro pakati pa vibwayila viŵiri vyauthenga, ndipo this is compared as an alternative to an idealized null hypothesis of no relationship between two data sets. Rejecting or disproving the null hypothesis is done using statistical tests that quantify the sense in which the null can be proven false, given the data that are used in the test. Working from a null hypothesis, two basic forms of error are recognized: Type I errors (null hypothesis is falsely rejected giving a "false positive") and Type II errors (null hypothesis fails to be rejected and an actual relationship between populations is missed giving a "false negative").

Statistical measurement processes are also prone to error in regards to the data that they generate. Many of these errors are classified as random (noise) or systematic (bias), but other types of errors (e.g., blunder, such as when an analyst reports incorrect units) can also occur. The presence of missing data or censoring may result in biased estimates and specific techniques have been developed to address these problems.

Vyakudanga

Statistics is a mathematical body of science that pertains to the collection, analysis, interpretation or explanation, and presentation of data, or as a branch of mathematics. Some consider statistics to be a distinct mathematical science rather than a branch of mathematics. While many scientific investigations make use of data, statistics is concerned with the use of data in the context of uncertainty and decision-making in the face of uncertainty.

In applying statistics to a problem, it is common practice to start with a population or process to be studied. Populations can be diverse topics, such as "all people living in a country" or "every atom composing a crystal". Ideally, statisticians compile data about the entire population (an operation called a census). This may be organized by governmental statistical institutes. Descriptive statistics can be used to summarize the population data. Numerical descriptors include mean and standard deviation for continuous data (like income), while frequency and percentage are more useful in terms of describing categorical data (like education).

When a census is not feasible, a chosen subset of the population called a sample is studied. Once a sample that is representative of the population is determined, data is collected for the sample members in an observational or experimental setting. Again, descriptive statistics can be used to summarize the sample data. However, drawing the sample contains an element of randomness; hence, the numerical descriptors from the sample are also prone to uncertainty. To draw meaningful conclusions about the entire population, inferential statistics are needed. It uses patterns in the sample data to draw inferences about the population represented while accounting for randomness. These inferences may take the form of answering yes/no questions about the data (hypothesis testing), estimating numerical characteristics of the data (estimation), describing associations within the data (correlation), and modeling relationships within the data (for example, using regression analysis). Inference can extend to the forecasting, prediction, and estimation of unobserved values either in or associated with the population being studied. It can include extrapolation and interpolation of time series or spatial data, as well as data mining.

Mathematical statistics

Mathematical statistics is the application of mathematics to statistics. Mathematical techniques used for this include mathematical analysis, linear algebra, stochastic analysis, differential equations, and measure-theoretic probability theory.

Mbiri

Formal discussions on inference date back to Arab mathematicians and cryptographers, during the Islamic Golden Age between the 8th and 13th centuries. Al-Khalil (717–786) wrote the Book of Cryptographic Messages, which contains one of the first uses of permutations and combinations, to list all possible Arabic words with and without vowels. Al-Kindi's Manuscript on Deciphering Cryptographic Messages gave a detailed description of how to use frequency analysis to decipher encrypted messages, providing an early example of statistical inference for decoding. Ibn Adlan (1187–1268) later made an important contribution on the use of sample size in frequency analysis.

The term 'statistic' was introduced by the Italian scholar Girolamo Ghilini in 1589 with reference to this science. The earliest writing containing statistics in Europe dates back to 1663, with the publication of Natural and Political Observations upon the Bills of Mortality by John Graunt. Early applications of statistical thinking revolved around the needs of states to base policy on demographic and economic data, hence its stat- etymology. The scope of the discipline of statistics broadened in the early 19th century to include the collection and analysis of data in general. Today, statistics is widely employed in government, business, and natural and social sciences.

The mathematical foundations of statistics developed from discussions concerning games of chance among mathematicians such as Gerolamo Cardano, Blaise Pascal, Pierre de Fermat, and Christiaan Huygens. Although the idea of probability was already examined in ancient and medieval law and philosophy (such as the work of Juan Caramuel), probability theory as a mathematical discipline only took shape at the very end of the 17th century, particularly in Jacob Bernoulli's posthumous work Ars Conjectandi. This was the first book where the realm of games of chance and the realm of the probable (which concerned opinion, evidence, and argument) were combined and submitted to mathematical analysis. The method of least squares was first described by Adrien-Marie Legendre in 1805, though Carl Friedrich Gauss presumably made use of it a decade earlier in 1795.

The modern field of statistics emerged in the late 19th and early 20th century in three stages. The first wave, at the turn of the century, was led by the work of Francis Galton and Karl Pearson, who transformed statistics into a rigorous mathematical discipline used for analysis, not just in science, but in industry and politics as well. Galton's contributions included introducing the concepts of standard deviation, correlation, regression analysis and the application of these methods to the study of the variety of human characteristics—height, weight and eyelash length among others. Pearson developed the Pearson product-moment correlation coefficient, defined as a product-moment, the method of moments for the fitting of distributions to samples and the Pearson distribution, among many other things. Galton and Pearson founded Biometrika as the first journal of mathematical statistics and biostatistics (then called biometry), and the latter founded the world's first university statistics department at University College London.

The second wave of the 1910s and 20s was initiated by William Sealy Gosset, and reached its culmination in the insights of Ronald Fisher, who wrote the textbooks that were to define the academic discipline in universities around the world. Fisher's most important publications were his 1918 seminal paper The Correlation between Relatives on the Supposition of Mendelian Inheritance (which was the first to use the statistical term, variance), his classic 1925 work Statistical Methods for Research Workers and his 1935 The Design of Experiments, where he developed rigorous design of experiments models. He originated the concepts of sufficiency, ancillary statistics, Fisher's linear discriminator and Fisher information. He also coined the term null hypothesis during the Lady tasting tea experiment, which "is never proved or established, but is possibly disproved, in the course of experimentation". In his 1930 book The Genetical Theory of Natural Selection, he applied statistics to various biological concepts such as Fisher's principle (which A. W. F. Edwards called "probably the most celebrated argument in evolutionary biology") and Fisherian runaway, a concept in sexual selection about a positive feedback runaway effect found in evolution.

The final wave, which mainly saw the refinement and expansion of earlier developments, emerged from the collaborative work between Egon Pearson and Jerzy Neyman in the 1930s. They introduced the concepts of "Type II" error, power of a test and confidence intervals. Jerzy Neyman in 1934 showed that stratified random sampling was in general a better method of estimation than purposive (quota) sampling.

Today, statistical methods are applied in all fields that involve decision making, for making accurate inferences from a collated body of data and for making decisions in the face of uncertainty based on statistical methodology. The use of modern computers has expedited large-scale statistical computations and has also made possible new methods that are impractical to perform manually. Statistics continues to be an area of active research, for example on the problem of how to analyze big data.

Mauthenga gha Kusanthura-Maŵiro

Kutolela uthenga

Kutolela Viyezgero
When full census data cannot be collected, statisticians collect sample data by developing specific experiment designs and survey samples. Statistics itself also provides tools for prediction and forecasting through statistical models.

To use a sample as a guide to an entire population, it is important that it truly represents the overall population. Representative sampling assures that inferences and conclusions can safely extend from the sample to the population as a whole. A major problem lies in determining the extent that the sample chosen is actually representative. Statistics offers methods to estimate and correct for any bias within the sample and data collection procedures. There are also methods of experimental design that can lessen these issues at the outset of a study, strengthening its capability to discern truths about the population.

Sampling theory is part of the mathematical discipline of probability theory. Probability is used in mathematical statistics to study the sampling distributions of sample statistics and, more generally, the properties of statistical procedures. The use of any statistical method is valid when the system or population under consideration satisfies the assumptions of the method. The difference in point of view between classic probability theory and sampling theory is, roughly, that probability theory starts from the given parameters of a total population to deduce probabilities that pertain to samples. Statistical inference, however, moves in the opposite direction—inductively inferring from samples to the parameters of a larger or total population.

Experimental and observational studies
A common goal for a statistical research project is to investigate causality, and in particular to draw a conclusion on the effect of changes in the values of predictors or independent variables on dependent variables. There are two major types of causal statistical studies: experimental studies and observational studies. In both types of studies, the effect of differences of an independent variable (or variables) on the behavior of the dependent variable are observed. The difference between the two types lies in how the study is actually conducted. Each can be very effective.
An experimental study involves taking measurements of the system under study, manipulating the system, and then taking additional measurements using the same procedure to determine if the manipulation has modified the values of the measurements. In contrast, an observational study does not involve experimental manipulation. Instead, data are gathered and correlations between predictors and response are investigated. While the tools of data analysis work best on data from randomized studies, they are also applied to other kinds of data—like natural experiments and observational studies—for which a statistician would use a modified, more structured estimation method (e.g., Difference in differences estimation and instrumental variables, among many others) that produce consistent estimators.

Vifukufuku
The basic steps of a statistical experiment are:
 Planning the research, including finding the number of replicates of the study, using the following information:  preliminary estimates regarding the size of treatment effects, alternative hypotheses, and the estimated experimental variability. Consideration of the selection of experimental subjects and the ethics of research is necessary. Statisticians recommend that experiments compare (at least) one new treatment with a standard treatment or control, to allow an unbiased estimate of the difference in treatment effects.
 Design of experiments, using blocking to reduce the influence of confounding variables, and randomized assignment of treatments to subjects to allow unbiased estimates of treatment effects and experimental error. At this stage, the experimenters and statisticians write the experimental protocol that will guide the performance of the experiment and which specifies the primary analysis of the experimental data.
 Performing the experiment following the experimental protocol and analyzing the data following the experimental protocol.
 Further examining the data set in secondary analyses, to suggest new hypotheses for future study.
 Documenting and presenting the results of the study.

Experiments on human behavior have special concerns. The famous Hawthorne study examined changes to the working environment at the Hawthorne plant of the Western Electric Company. The researchers were interested in determining whether increased illumination would increase the productivity of the assembly line workers. The researchers first measured the productivity in the plant, then modified the illumination in an area of the plant and checked if the changes in illumination affected productivity. It turned out that productivity indeed improved (under the experimental conditions). However, the study is heavily criticized today for errors in experimental procedures, specifically for the lack of a control group and blindness. The Hawthorne effect refers to finding that an outcome (in this case, worker productivity) changed due to observation itself. Those in the Hawthorne study became more productive not because the lighting was changed but because they were being observed.

Kuŵazga Kwakulaŵilila
An example of an observational study is one that explores the association between smoking and lung cancer. This type of study typically uses a survey to collect observations about the area of interest and then performs statistical analysis. In this case, the researchers would collect observations of both smokers and non-smokers, perhaps through a cohort study, and then look for the number of cases of lung cancer in each group. A case-control study is another type of observational study in which people with and without the outcome of interest (e.g. lung cancer) are invited to participate and their exposure histories are collected.

Mitundu ya uthenga

Various attempts have been made to produce a taxonomy of levels of measurement. The psychophysicist Stanley Smith Stevens defined nominal, ordinal, interval, and ratio scales. Nominal measurements do not have meaningful rank order among values, and permit any one-to-one (injective) transformation. Ordinal measurements have imprecise differences between consecutive values, but have a meaningful order to those values, and permit any order-preserving transformation. Interval measurements have meaningful distances between measurements defined, but the zero value is arbitrary (as in the case with longitude and temperature measurements in Celsius or Fahrenheit), and permit any linear transformation. Ratio measurements have both a meaningful zero value and the distances between different measurements defined, and permit any rescaling transformation.

Because variables conforming only to nominal or ordinal measurements cannot be reasonably measured numerically, sometimes they are grouped together as categorical variables, whereas ratio and interval measurements are grouped together as quantitative variables, which can be either discrete or continuous, due to their numerical nature. Such distinctions can often be loosely correlated with data type in computer science, in that dichotomous categorical variables may be represented with the Boolean data type, polytomous categorical variables with arbitrarily assigned integers in the integral data type, and continuous variables with the real data type involving floating-point arithmetic. But the mapping of computer science data types to statistical data types depends on which categorization of the latter is being implemented.

Other categorizations have been proposed. For example, Mosteller and Tukey (1977) distinguished grades, ranks, counted fractions, counts, amounts, and balances. Nelder (1990) described continuous counts, continuous ratios, count ratios, and categorical modes of data. (See also: Chrisman (1998), van den Berg (1991).)

The issue of whether or not it is appropriate to apply different kinds of statistical methods to data obtained from different kinds of measurement procedures is complicated by issues concerning the transformation of variables and the precise interpretation of research questions. "The relationship between the data and what they describe merely reflects the fact that certain kinds of statistical statements may have truth values which are not invariant under some transformations. Whether or not a transformation is sensible to contemplate depends on the question one is trying to answer."

Nthowa

Descriptive statistics

A descriptive statistic (in the count noun sense) is a summary statistic that quantitatively describes or summarizes features of a collection of information, while descriptive statistics in the mass noun sense is the process of using and analyzing those statistics. Descriptive statistics is distinguished from inferential statistics (or inductive statistics), in that descriptive statistics aims to summarize a sample, rather than use the data to learn about the population that the sample of data is thought to represent.

Inferential statistics

Statistical inference is the process of using data analysis to deduce properties of an underlying probability distribution. Inferential statistical analysis infers properties of a population, for example by testing hypotheses and deriving estimates.  It is assumed that the observed data set is sampled from a larger population. Inferential statistics can be contrasted with descriptive statistics. Descriptive statistics is solely concerned with properties of the observed data, and it does not rest on the assumption that the data come from a larger population.

Terminology and theory of inferential statistics

Statistics, estimators and pivotal quantities
Consider independent identically distributed (IID) random variables with a given probability distribution: standard statistical inference and estimation theory defines a random sample as the random vector given by the column vector of these IID variables. The population being examined is described by a probability distribution that may have unknown parameters.

A statistic is a random variable that is a function of the random sample, but . The probability distribution of the statistic, though, may have unknown parameters. Consider now a function of the unknown parameter: an estimator is a statistic used to estimate such function. Commonly used estimators include sample mean, unbiased sample variance and sample covariance.

A random variable that is a function of the random sample and of the unknown parameter, but whose probability distribution does not depend on the unknown parameter is called a pivotal quantity or pivot. Widely used pivots include the z-score, the chi square statistic and Student's t-value.

Between two estimators of a given parameter, the one with lower mean squared error is said to be more efficient. Furthermore, an estimator is said to be unbiased if its expected value is equal to the true value of the unknown parameter being estimated, and asymptotically unbiased if its expected value converges at the limit to the true value of such parameter.

Other desirable properties for estimators include: UMVUE estimators that have the lowest variance for all possible values of the parameter to be estimated (this is usually an easier property to verify than efficiency) and consistent estimators which converges in probability to the true value of such parameter.

This still leaves the question of how to obtain estimators in a given situation and carry the computation, several methods have been proposed: the method of moments, the maximum likelihood method, the least squares method and the more recent method of estimating equations.

Null hypothesis and alternative hypothesis
Interpretation of statistical information can often involve the development of a null hypothesis which is usually (but not necessarily) that no relationship exists among variables or that no change occurred over time.

The best illustration for a novice is the predicament encountered by a criminal trial. The null hypothesis, H0, asserts that the defendant is innocent, whereas the alternative hypothesis, H1, asserts that the defendant is guilty. The indictment comes because of suspicion of the guilt. The H0 (status quo) stands in opposition to H1 and is maintained unless H1 is supported by evidence "beyond a reasonable doubt". However, "failure to reject H0" in this case does not imply innocence, but merely that the evidence was insufficient to convict. So the jury does not necessarily accept H0 but fails to reject H0. While one can not "prove" a null hypothesis, one can test how close it is to being true with a power test, which tests for type II errors.

What statisticians call an alternative hypothesis is simply a hypothesis that contradicts the null hypothesis.

Error
Working from a null hypothesis, two broad categories of error are recognized:
 Type I errors where the null hypothesis is falsely rejected, giving a "false positive".
 Type II errors where the null hypothesis fails to be rejected and an actual difference between populations is missed, giving a "false negative".

Standard deviation refers to the extent to which individual observations in a sample differ from a central value, such as the sample or population mean, while Standard error refers to an estimate of difference between sample mean and population mean.

A statistical error is the amount by which an observation differs from its expected value. A residual is the amount an observation differs from the value the estimator of the expected value assumes on a given sample (also called prediction).

Mean squared error is used for obtaining efficient estimators, a widely used class of estimators. Root mean square error is simply the square root of mean squared error.

Many statistical methods seek to minimize the residual sum of squares, and these are called "methods of least squares" in contrast to Least absolute deviations. The latter gives equal weight to small and big errors, while the former gives more weight to large errors. Residual sum of squares is also differentiable, which provides a handy property for doing regression. Least squares applied to linear regression is called ordinary least squares method and least squares applied to nonlinear regression is called non-linear least squares. Also in a linear regression model the non deterministic part of the model is called error term, disturbance or more simply noise. Both linear regression and non-linear regression are addressed in polynomial least squares, which also describes the variance in a prediction of the dependent variable (y axis) as a function of the independent variable (x axis) and the deviations (errors, noise, disturbances) from the estimated (fitted) curve.

Measurement processes that generate statistical data are also subject to error.  Many of these errors are classified as random (noise) or systematic (bias), but other types of errors (e.g., blunder, such as when an analyst reports incorrect units) can also be important. The presence of missing data or censoring may result in biased estimates and specific techniques have been developed to address these problems.

Interval estimation

Most studies only sample part of a population, so results do not fully represent the whole population. Any estimates obtained from the sample only approximate the population value. Confidence intervals allow statisticians to express how closely the sample estimate matches the true value in the whole population. Often they are expressed as 95% confidence intervals. Formally, a 95% confidence interval for a value is a range where, if the sampling and analysis were repeated under the same conditions (yielding a different dataset), the interval would include the true (population) value in 95% of all possible cases. This does not imply that the probability that the true value is in the confidence interval is 95%. From the frequentist perspective, such a claim does not even make sense, as the true value is not a random variable.  Either the true value is or is not within the given interval. However, it is true that, before any data are sampled and given a plan for how to construct the confidence interval, the probability is 95% that the yet-to-be-calculated interval will cover the true value: at this point, the limits of the interval are yet-to-be-observed random variables. One approach that does yield an interval that can be interpreted as having a given probability of containing the true value is to use a credible interval from Bayesian statistics: this approach depends on a different way of interpreting what is meant by "probability", that is as a Bayesian probability.

In principle confidence intervals can be symmetrical or asymmetrical. An interval can be asymmetrical because it works as lower or upper bound for a parameter (left-sided interval or right sided interval), but it can also be asymmetrical because the two sided interval is built violating symmetry around the estimate. Sometimes the bounds for a confidence interval are reached asymptotically and these are used to approximate the true bounds.

Significance

Statistics rarely give a simple Yes/No type answer to the question under analysis. Interpretation often comes down to the level of statistical significance applied to the numbers and often refers to the probability of a value accurately rejecting the null hypothesis (sometimes referred to as the p-value).

The standard approach is to test a null hypothesis against an alternative hypothesis. A critical region is the set of values of the estimator that leads to refuting the null hypothesis. The probability of type I error is therefore the probability that the estimator belongs to the critical region given that null hypothesis is true (statistical significance) and the probability of type II error is the probability that the estimator does not belong to the critical region given that the alternative hypothesis is true. The statistical power of a test is the probability that it correctly rejects the null hypothesis when the null hypothesis is false.

Referring to statistical significance does not necessarily mean that the overall result is significant in real world terms. For example, in a large study of a drug it may be shown that the drug has a statistically significant but very small beneficial effect, such that the drug is unlikely to help the patient noticeably.

Although in principle the acceptable level of statistical significance may be subject to debate, the significance level is the largest p-value that allows the test to reject the null hypothesis. This test is logically equivalent to saying that the p-value is the probability, assuming the null hypothesis is true, of observing a result at least as extreme as the test statistic. Therefore, the smaller the significance level, the lower the probability of committing type I error.

Some problems are usually associated with this framework (See criticism of hypothesis testing):
 A difference that is highly statistically significant can still be of no practical significance, but it is possible to properly formulate tests to account for this. One response involves going beyond reporting only the significance level to include the p-value when reporting whether a hypothesis is rejected or accepted. The p-value, however, does not indicate the size or importance of the observed effect and can also seem to exaggerate the importance of minor differences in large studies. A better and increasingly common approach is to report confidence intervals. Although these are produced from the same calculations as those of hypothesis tests or p-values, they describe both the size of the effect and the uncertainty surrounding it.
 Fallacy of the transposed conditional, aka prosecutor's fallacy: criticisms arise because the hypothesis testing approach forces one hypothesis (the null hypothesis) to be favored, since what is being evaluated is the probability of the observed result given the null hypothesis and not probability of the null hypothesis given the observed result. An alternative to this approach is offered by Bayesian inference, although it requires establishing a prior probability.
 Rejecting the null hypothesis does not automatically prove the alternative hypothesis.
 As everything in inferential statistics it relies on sample size, and therefore under fat tails p-values may be seriously mis-computed.

Examples
Some well-known statistical tests and procedures are:

Exploratory data analysis

Exploratory data analysis (EDA) is an approach to analyzing data sets to summarize their main characteristics, often with visual methods. A statistical model can be used or not, but primarily EDA is for seeing what the data can tell us beyond the formal modeling or hypothesis testing task.

Misuse

Misuse of statistics can produce subtle but serious errors in description and interpretation—subtle in the sense that even experienced professionals make such errors, and serious in the sense that they can lead to devastating decision errors. For instance, social policy, medical practice, and the reliability of structures like bridges all rely on the proper use of statistics.

Even when statistical techniques are correctly applied, the results can be difficult to interpret for those lacking expertise. The statistical significance of a trend in the data—which measures the extent to which a trend could be caused by random variation in the sample—may or may not agree with an intuitive sense of its significance. The set of basic statistical skills (and skepticism) that people need to deal with information in their everyday lives properly is referred to as statistical literacy.

There is a general perception that statistical knowledge is all-too-frequently intentionally misused by finding ways to interpret only the data that are favorable to the presenter. A mistrust and misunderstanding of statistics is associated with the quotation, "There are three kinds of lies: lies, damned lies, and statistics". Misuse of statistics can be both inadvertent and intentional, and the book How to Lie with Statistics, by Darrell Huff, outlines a range of considerations. In an attempt to shed light on the use and misuse of statistics, reviews of statistical techniques used in particular fields are conducted (e.g. Warne, Lazo, Ramos, and Ritter (2012)).

Ways to avoid misuse of statistics include using proper diagrams and avoiding bias. Misuse can occur when conclusions are overgeneralized and claimed to be representative of more than they really are, often by either deliberately or unconsciously overlooking sampling bias. Bar graphs are arguably the easiest diagrams to use and understand, and they can be made either by hand or with simple computer programs. Unfortunately, most people do not look for bias or errors, so they are not noticed. Thus, people may often believe that something is true even if it is not well represented. To make data gathered from statistics believable and accurate, the sample taken must be representative of the whole. According to Huff, "The dependability of a sample can be destroyed by [bias]... allow yourself some degree of skepticism."

To assist in the understanding of statistics Huff proposed a series of questions to be asked in each case:
 Who says so? (Does he/she have an axe to grind?)
 How does he/she know? (Does he/she have the resources to know the facts?)
 What's missing? (Does he/she give us a complete picture?)
 Did someone change the subject? (Does he/she offer us the right answer to the wrong problem?)
 Does it make sense? (Is his/her conclusion logical and consistent with what we already know?)

Misinterpretation: correlation

The concept of correlation is particularly noteworthy for the potential confusion it can cause. Statistical analysis of a data set often reveals that two variables (properties) of the population under consideration tend to vary together, as if they were connected. For example, a study of annual income that also looks at age of death, might find that poor people tend to have shorter lives than affluent people. The two variables are said to be correlated; however, they may or may not be the cause of one another. The correlation phenomena could be caused by a third, previously unconsidered phenomenon, called a lurking variable or confounding variable. For this reason, there is no way to immediately infer the existence of a causal relationship between the two variables.

Applications

Applied statistics, theoretical statistics and mathematical statistics
Applied statistics, sometimes referred to as Statistical science, comprises descriptive statistics and the application of inferential statistics. Theoretical statistics concerns the logical arguments underlying justification of approaches to statistical inference, as well as encompassing mathematical statistics. Mathematical statistics includes not only the manipulation of probability distributions necessary for deriving results related to methods of estimation and inference, but also various aspects of computational statistics and the design of experiments.

Statistical consultants can help organizations and companies that do not have in-house expertise relevant to their particular questions.

Machine learning and data mining
Machine learning models are statistical and probabilistic models that capture patterns in the data through use of computational algorithms.

Statistics in academia
Statistics is applicable to a wide variety of academic disciplines, including natural and social sciences, government, and business. Business statistics applies statistical methods in econometrics, auditing and production and operations, including services improvement and marketing research. A study of two journals in tropical biology found that the 12 most frequent statistical tests are: analysis of variance (ANOVA), chi-squared test, Student's t-test, linear regression, Pearson's correlation coefficient, Mann-Whitney U test, Kruskal-Wallis test, Shannon's diversity index, Tukey's range test, cluster analysis, Spearman's rank correlation coefficient and principal component analysis.

A typical statistics course covers descriptive statistics, probability, binomial and normal distributions, test of hypotheses and confidence intervals, linear regression, and correlation. Modern fundamental statistical courses for undergraduate students focus on correct test selection, results interpretation, and use of free statistics software.

Statistical computing

The rapid and sustained increases in computing power starting from the second half of the 20th century have had a substantial impact on the practice of statistical science. Early statistical models were almost always from the class of linear models, but powerful computers, coupled with suitable numerical algorithms, caused an increased interest in nonlinear models (such as neural networks) as well as the creation of new types, such as generalized linear models and multilevel models.

Increased computing power has also led to the growing popularity of computationally intensive methods based on resampling, such as permutation tests and the bootstrap, while techniques such as Gibbs sampling have made use of Bayesian models more feasible. The computer revolution has implications for the future of statistics with a new emphasis on "experimental" and "empirical" statistics. A large number of both general and special purpose statistical software are now available. Examples of available software capable of complex statistical computation include programs such as Mathematica, SAS, SPSS, and R.

Business statistics
In business, "statistics" is a widely used management- and decision support tool. It is particularly applied in financial management, marketing management, and production, services and operations management . Statistics is also heavily used in management accounting and auditing. The discipline of Management Science formalizes the use of statistics, and other mathematics, in business. (Econometrics is the application of statistical methods to economic data in order to give empirical content to economic relationships.)

A typical "Business Statistics" course is intended for business majors, and covers  descriptive statistics (collection, description, analysis, and summary of data), probability (typically the binomial and normal distributions), test of hypotheses and confidence intervals, linear regression, and correlation; (follow-on) courses may include forecasting, time series, decision trees, multiple linear regression, and other topics from business analytics more generally. See also . Professional certification programs, such as the CFA, often include topics in statistics.

Statistics applied to mathematics or the arts
Traditionally, statistics was concerned with drawing inferences using a semi-standardized methodology that was "required learning" in most sciences. This tradition has changed with the use of statistics in non-inferential contexts. What was once considered a dry subject, taken in many fields as a degree-requirement, is now viewed enthusiastically. Initially derided by some mathematical purists, it is now considered essential methodology in certain areas.
 In number theory, scatter plots of data generated by a distribution function may be transformed with familiar tools used in statistics to reveal underlying patterns, which may then lead to hypotheses.
 Predictive methods of statistics in forecasting combining chaos theory and fractal geometry can be used to create video works.
 The process art of Jackson Pollock relied on artistic experiments whereby underlying distributions in nature were artistically revealed. With the advent of computers, statistical methods were applied to formalize such distribution-driven natural processes to make and analyze moving video art.
 Methods of statistics may be used predicatively in performance art, as in a card trick based on a Markov process that only works some of the time, the occasion of which can be predicted using statistical methodology.
 Statistics can be used to predicatively create art, as in the statistical or stochastic music invented by Iannis Xenakis, where the music is performance-specific. Though this type of artistry does not always come out as expected, it does behave in ways that are predictable and tunable using statistics.

Specialized disciplines

Statistical techniques are used in a wide range of types of scientific and social research, including: biostatistics, computational biology, computational sociology, network biology, social science, sociology and social research. Some fields of inquiry use applied statistics so extensively that they have specialized terminology. These disciplines include:

In addition, there are particular types of statistical analysis that have also developed their own specialised terminology and methodology:

Statistics form a key basis tool in business and manufacturing as well. It is used to understand measurement systems variability, control processes (as in statistical process control or SPC), for summarizing data, and to make data-driven decisions. In these roles, it is a key tool, and perhaps the only reliable tool.

See also

Foundations and major areas of statistics

References

Further reading
 Lydia Denworth, "A Significant Problem: Standard scientific methods are under fire. Will anything change?", Scientific American, vol. 321, no. 4 (October 2019), pp. 62–67. "The use of p values for nearly a century [since 1925] to determine statistical significance of experimental results has contributed to an illusion of certainty and [to] reproducibility crises in many scientific fields. There is growing determination to reform statistical analysis... Some [researchers] suggest changing statistical methods, whereas others would do away with a threshold for defining "significant" results." (p. 63.)

 OpenIntro Statistics , 3rd edition by Diez, Barr, and Cetinkaya-Rundel
 Stephen Jones, 2010. Statistics in Psychology: Explanations without Equations. Palgrave Macmillan. .

External links

 (Electronic Version): TIBCO Software Inc. (2020). Data Science Textbook.
 Online Statistics Education: An Interactive Multimedia Course of Study. Developed by Rice University (Lead Developer), University of Houston Clear Lake, Tufts University, and National Science Foundation.
 UCLA Statistical Computing Resources (archived 17 July 2006)
 Philosophy of Statistics from the Stanford Encyclopedia of Philosophy

Data
Formal sciences
Information
Mathematical and quantitative methods (economics)
Research methods
Arab inventions

Kusanthura-Maŵiro


James Thorington (May 7, 1816 –  June 13, 1887) was a frontiersman, lawyer, judge, and one-term U.S. Representative from Iowa's 2nd congressional district.

Biography
Born in Wilmington, North Carolina, Thorington moved with his parents to Montgomery, Alabama, in 1827.  He attended the common schools, the military school in Fayetteville, North Carolina from 1830 to 1832, and the University of Alabama at Tuscaloosa from 1832 to 1835.

He studied law in Montgomery, Alabama. He interrupted his studies to trap and trade on the upper Missouri and Columbia Rivers from 1837 to 1839.  He then moved to Davenport, Iowa, in 1839.  After winning election as Davenport's mayor in 1843, he was admitted to the bar in 1844, commenced practice in Davenport, and remained as mayor until 1847.  He was probate judge of Scott County, Iowa from 1843 to 1851, and the clerk of the district court from 1846 to 1854.

In 1854, Thorington was elected as a Whig to the Thirty-fourth Congress (March 4, 1855 – March 3, 1857). While he was in Congress, the Iowa Republican Party was founded, and he was a charter member. For that reason "he has been styled as the first Republican congressman from Iowa."
In 1856, he was a candidate for the Republican Party's nomination for his seat, but lost at the district convention on the ninth ballot to Timothy Davis, who would go on to win the general election.

After his term ended, Thorington became Scott County's sheriff from 1859 to 1863, and its recorder from 1864 to 1868.

He was appointed consul at Aspinwall, Colombia, on January 21, 1873. He was appointed commercial agent at the same city on May 27, 1873, and served in both positions until October 21, 1882.

He died while on a visit to his daughter at Santa Fe, New Mexico Territory, on June 13, 1887.  He was interred in Oakdale Cemetery in Davenport.

References

1816 births
1887 deaths
Iowa lawyers
Iowa state court judges
Iowa Whigs
Politicians from Wilmington, North Carolina
Politicians from Davenport, Iowa
Whig Party members of the United States House of Representatives
Republican Party members of the United States House of Representatives from Iowa
Mayors of Davenport, Iowa
19th-century American politicians
19th-century American judges
19th-century American lawyers

James Thorington


Bigoli  (Venetian: bìgołi) is an extruded pasta in the form of a long and thick strand. Initially bigoli were made with buckwheat flour, but are now more commonly made with whole wheat flour, and sometimes include duck eggs. The preparation is then extruded through a bigolaro, from which the pasta gets its name.

Bigoli is a term used in Veneto; a similar type of pasta called pici is produced in Tuscany.

History
There are different versions of the origins of the bigoli. They only agree that they originated in what is now the Veneto region. According to one theory, its origin dates back to the 14th century during the Venetian Turkish Wars. After the Turks sank numerous Venetian ships loaded with durum, the remaining flour was stretched with common wheat flour. The new mixture was used for a dough, formed into a large spaghetto and called a bigolo.

In 1604, a pasta maker from Padua named Bartolomio Veronese, known as Abbondanza, patented a press for making bigoli. This was the real triumph of the bigoli.

According to another version, the bigoli are the result of a further development of a type of pasta that was already widespread in Northeast Italy. They were first mentioned as bigoli in the 15th century at the court of the Bishop of Eraclea.

See also
Bigoli in salsa
Macaroni
Venetian cuisine
Pici

References

Types of pasta
Cuisine of Veneto

Bigoli


Adolfo Fumagalli (19 October 18283 May 1856) was a 19th-century Italian virtuoso pianist and composer, known today primarily for his virtuosic compositions for the left hand alone.

Born in Inzago, Italy, he grew up in a very musically oriented environment. He had three brothers who also became musicians and composers, these being Carlo (1822-1907), Luca (1837 - 1908), Disma (1826 - 1893) and Polibio (1830 - 1901). Fumagalli studied music with Angeloni at the Milan Conservatory and, in 1848, at the age of 20, made his Milan debut with some success. He then travelled to Turin, Paris, Belgium and Denmark, playing his own operatic fantasies and other salon works to great acclaim.

In 1856 he returned to Italy and, when he arrived, was soon thereafter given an Erard grand piano from the firm as an advertising promotion. On 1 May that year he gave a concert but, shortly after, fell ill and died days later in Florence.

He created his greatest sensation when he began performing his works for left hand. Although he looked rather frail, as is evident from paintings of him, he had a phenomenal technique and strong fingers that astonished everyone.

Fumagalli's output is quite extensive, though almost all of it is extremely difficult to obtain today. His works consist primarily of operatic fantasies and character pieces. One of his most difficult and virtuosic works is his Grande Fantasie sur Robert le Diable de Meyerbeer, op.106 (dedicated to Liszt) for the left hand. He also composed an arrangement of Vincenzo Bellini's "Casta Diva" from Norma for the left hand. Almost his entire output is for solo piano and the works which employ other instruments all seem to include the piano in some way, a feature that is similar to Chopin's output. Although he was perhaps not a very inspired or ingenious composer, his works for left hand alone stand nonetheless as an important testament of the progress in technique and virtuosity of the period, especially of single-handed works.

Musical works
List of works:
Op. 1 Fantaisie on motives from Verdi's opera Nabuccodonosor for piano
Op. 2 Notturno-Studio for left hand
Op. 3 The Devil's Galop for piano
Op. 4a Reminiscences of Meyerbeer's opera Robert le Diable for piano
Op. 6 Tarantelle for piano
Op. 8 La fucina di Vulcano/ Il Canto dei Ciclopi : scherzo fantastique for piano
Op. 11 Caprice romantique for piano
Op. 12 Nocturne sentimentale in Ab Major for piano
Op. 13 Il genio della danza : scherzo brillant for piano
Op. 14 Grande fantaisie on motives from Bellini's La Sonnambula for piano
Op. 16 Pensée pathétique for piano
Op. 17 Nocturnino for piano
Op. 18
No.1 Studio da Concerto based on Fra poco a me ricovero from Donizetti's opera Lucia di Lammermoor for left hand
No.2 Studio da Concerto based on Coro O Signore del tetto natio from Verdi's opera I Lombardi for left hand
Op. 20 Les trois soeurs : petites fantaisies for piano
No.1 Based on Verdi's opera Attila
No.2 Based on Verdi's opera Foscari
No.3 Based on Verdi's opera Ernani
Op. 21 Les clochettes : grande concerto fantastique pour piano avec l'accompagnement d'un grand orchestra et une campanella
Op. 23 Quatres airs de ballet variés from Verdi's opera Jérusalem for piano
No.1 Pas de Quatre
No.2 Pas de Deux
No.3 Pas Seul
No.4 Pas d'Ensemble
Op. 26 Grande Fantaisie Drammatique on motives from Donizetti's opera Lucia di Lammermoor  for piano
Op. 27 Grande Caprice de Concert for piano
Op. 28 Grande Fantasie on Bellini's opera I Puritani (Dedicated to his brother Polibio for piano
Op. 29 Nenna : Tarantella Giocosa for piano
Op. 30 Grande Fantaisie on Bellini's opera Norma for piano
Op. 31 Petit morceau de salon on Verdi's opera Macbeth for piano
Op. 32 Petit morceau de salon on Verdi's opera La Battaglia di Legnano for piano
Op. 33 La pendule : caprice fantastique contenant un galop-carillon et un polka-mazurka for piano
Op. 34 Petite Fantaisie on Verdi's opera Lucrezia Borgia for piano
Op. 35 Petite Fantaisie on Donizetti's opera Elisir d'amore for piano
Op. 36 Beatrice di tenda : petit morceau de salon for piano
Op. 37 Souvenir de Nice : polka-caprice for piano
Op. 38 Nocturne: Une Nuit d'Été, passetemps sentimental for piano
Op. 39 Amorosa : mazurka sentimentale for piano
Op. 40 La capricciosa : Tyrolienne for piano
Op. 41 Morceau de salon : chanson espagnole from Rossi's opera Il domino nero for piano
Op. 42 Morceau de salon on Rossi's opera Il domino nero for piano
Op. 43 Le prophete : grande fantaisie de bravoure for piano
Op. 44 La serenade espagnole : morceau elegant for piano
Op. 45 Fantaisie on Bonoldi's opera Nera Orientale for piano
Op. 47 Le Postillon : galop de concert for piano
Op. 48 Le Ruisseau : etude impromptu for piano
Op. 49 Grande Marche cosaque on a national air for piano
Op. 50 Serenade napolitaine for piano
Op. 51 Le Streghe : pièce fantastique for piano
Op. 52 Musical Recreations: two divertimenti for piano on motives from Verdi's opera Luisa Miller
No.1 Premier Divertimento
No.2 Deuxième Divertimento
Op. 53 Esprits Folles : saltarelle for piano
Op. 54 Fantaisie on Donizetti's opera Linda de Chamounix for piano
Op. 55 Stabat Mater by Rossini for piano
Op. 56 Fantaisie on Bellini's opera La Straniera for piano
Op. 57 Si loin! : Mélody by Paul Henrion variée for piano
Op. 58 Luisa : polka de concert for piano
Op. 59 Fantaisie on a melody from Verdi's opera Stiffelio
Op. 60 Grande Fantaisie Militaire for piano
No.1 Ronda Notturna for piano
No.2 Una notte al campo for piano
No.3 Signal d'alarme et conflit de guerre from Bellini's opera Norma for piano
No.4 Marcia funèbre for piano
No.5 Inno trionfale from Rossini's opera Le Siège de Corinthe for piano
No.6 Orgia for piano
Op. 60 Grande Fantaisie Militaire transcribed for four hands by the author
Op. 61 Casta diva from Bellini's opera Norma for left hand
Op. 62 La sacrilega parola : Variations on the Grande Adagio Finale from the 2nd act of Donizetti's opera Poliuto for piano
Op. 63 Souvenir de Chopin : mazurka for piano
Op. 64 La Derelitta : pensée romantique for piano
Op. 65 La festa dell'innocenza : cinque morceaux brillants for piano
Op. 66 Fantasie brillante on motives from Donizetti's opera Poliuto for piano
Op. 68 Introduction et Grande Nocturne on Sanelli's opera Il Fornaretto for piano
Op. 69 La Baccante : caprice burlesque for piano
Op. 70 Sogno d'amore : pensée fugitive for piano
Op. 71 Morceau de Salon : caprice on Chiaromonte's opera Il Gondoliero for piano
Op. 72 Fantaisie Brillante on Verdi's opera I Due Foscari for piano
Op. 73 Nocturne variée on the romanza Fior di bonta bell'angelo from Villanis's opera La Regina di Leone for piano
Op. 74 Fantaisie Brillante on Verdi's opera Ernani for piano
Op. 75 I Lombardi alla prima Crociata : introduction et grande adagio variées sur la terzette "Qual volutta trascorrere" for piano
Op. 76 Laura : polonaise de concert for piano
Op. 77 Saluto al Tamigi : deuxième polka de concert, capriccio-impromptu for piano
Op. 78 Un lamento : deuxième mazurka sentimentale for piano
Op. 79 L' Absence : romance variée for piano
Op. 80 La Chasse : morceau brillant for piano
Op. 81 Grande Ouverture de Benvenuto Cellini par Hector Berlioz : transcrite pour piano
Op. 82 Nocturne elegant for piano
Op. 83 La danse des sylphes, de Felix Godefroid : rondo brillant for piano
Op. 84 Grande Fantaisie on Bellini's opera I Puritani for two pianos
Op. 85 Preghiera alla Madonna "O Santissima Vergine" : Popular Tuscan song by L. Gordigiani transcribed for piano
Op. 86 L' Étincelle : reverie de F. Bonoldi variée pour piano
Op. 87 La buena ventura : chanson andalouse de Yradier variée for piano
Op. 88 La cloche : mélodie de F. Bonoldi variée pour piano
Op. 89 Introduction et adagio varié on the romanza "Sempre all'alba ed alla sera" from the opera Giovanna d'Arco for piano
Op. 90 Le Palmier : polka des magots for piano
Op. 91 Fantaisie on Verdi's Nabucodonosor for piano
Op. 92 Paraphrase on the barcarolle Una Barchetta in Mar from Donizetti's opera Gianni di Calais for piano
Op. 94 Paraphrase on the Grande adagio finale from Coccia's opera La solitaria delle Asturie for piano
Op. 95 Un carnaval de plus, souvenir de Venice : Caprice de Concert for piano
Op. 95b Fantaisie on Verdi's opera Il Trovatore for piano
Op. 98 Fantaisie on Verdi's opera La Traviata for piano
Op. 100 École Moderne du Pianiste : recueil de 24 morceaux caracteristiques for piano
Op. 101 Tarantelle de bravoure on Thomas's opera La Tonelli for piano
Op. 102 Mi mancha la voce (Andante) from Rossini's opera Mosé in Egitto for left hand
Op. 103 Cantique de Noel for piano
Op. 104 Berceuse for piano
Op. 105 L' Échange : ariette for piano
Op. 106 Grande Fantasie sur Robert le Diable de Meyerbeer (Dedicated to Franz Liszt) for left hand
Op. 107 posth. Mon Ange : mélodie d'Auguste Morel transcrit pour piano
Op. 108 posth. Illustrations from Verdi's opera Giovanna de Guzman (I Vespri Siciliani) for piano
Op. 108 Premier Boléro
Op. 109 posth. Ariele : nocturne variée from Leoni's opera Suddetta for piano
Op. 110 Enfants, n'y touchez pas : romance for piano
Op. 111 Paraphrase on Buzzolla's barcarolle Tace il vento in ciel sereno for piano
Op. 112 posth. Duettino "Presso alla tomba" (the author's last work) for piano

Also included in his output are several songs for voice and piano.

References

External links

 Grande Fantaisie sur Robert le Diable,  for piano left hand, Op.106 played by Artur Cimirro on YouTube

1828 births
1856 deaths
19th-century classical composers
19th-century classical pianists
19th-century Italian male musicians
Italian Romantic composers
Italian classical composers
Italian male classical composers
Italian classical pianists
Italian male pianists
Male classical pianists
Classical pianists who played with one arm
Milan Conservatory alumni
People from the Province of Milan

Adolfo Fumagalli


A Universally Unique Identifier (UUID) is a 128-bit label used for information in computer systems. The term Globally Unique Identifier (GUID) is also used, mostly in Microsoft systems.

When generated according to the standard methods, UUIDs are, for practical purposes, unique. Their uniqueness does not depend on a central registration authority or coordination between the parties generating them, unlike most other numbering schemes. While the probability that a UUID will be duplicated is not zero, it is generally considered close enough to zero to be negligible.

Thus, anyone can create a UUID and use it to identify something with near certainty that the identifier does not duplicate one that has already been, or will be, created to identify something else. Information labeled with UUIDs by independent parties can therefore be later combined into a single database or transmitted on the same channel, with a negligible probability of duplication.

Adoption of UUIDs is widespread, with many computing platforms providing support for generating them and for parsing their textual representation.

History

In the 1980s Apollo Computer originally used UUIDs in the Network Computing System (NCS). Later, the Open Software Foundation (OSF) used UUIDs for their Distributed Computing Environment (DCE). The design of the DCE UUIDs was partly based on the NCS UUIDs, whose design was in turn inspired by the (64-bit) unique identifiers defined and used pervasively in Domain/OS, an operating system designed by Apollo Computer. Later, the Microsoft Windows platforms adopted the DCE design as "Globally Unique IDentifiers" (GUIDs).

 registered a URN namespace for UUIDs and recapitulated the earlier specifications, with the same technical content.
When in July 2005  was published as a proposed IETF standard, the ITU had also standardized UUIDs, based on the previous standards and early versions of .

Standards

UUIDs are standardized by the Open Software Foundation (OSF) as part of the Distributed Computing Environment (DCE).

UUIDs are documented as part of ISO/IEC 11578:1996 "Information technology – Open Systems Interconnection – Remote Procedure Call (RPC)" and more recently in ITU-T Rec. X.667 | ISO/IEC 9834-8:2014.

The Internet Engineering Task Force (IETF) published the Standards-Track , technically equivalent to ITU-T Rec. X.667 | ISO/IEC 9834-8. The "Revise Universally Unique Identifier Definitions Working Group" is working on an update which will introduce additional versions.

Binary wire format

A UUID is a 128 bit label. Initially, Apollo Computer designed the UUID with the following wire format:

{| class="wikitable"
|+ The legacy wire format
! Name
! Offset
! Length
! Description
|-
| time_high
| 0x00
| 4 octets / 32 bits
| The first 6 octets are the number of 4 µsec units of time that have passed since 1980-01-01, 0000 UTC.
|-
| time_low
| 0x04
| 2 octets / 16 bits
| See above.
|-
| reserved
| 0x06
| 2 octets / 16 bits
|These octets are reserved for future use.
|-
| family
| 0x08
| 1 octet / 8 bits
| This octet is an address family.
|-
| node
| 0x09
| 7 octets / 56 bits
| These octets are a host ID in the form allowed by the specified address family.
|}

Later, the UUID was extended by coinciding the legacy family field with the new variant field. Because the family field only had used the values ranging from 0–13 in the past, it was decided that a UUID with the most significant bit set to 0 was a legacy UUID. This gives the following table:

{| class="wikitable"
|+ Family / variant field
! MSb 0
! MSb 1
! MSb 2
! Legacy family field value range
! Description
|-
| 0
| x
| x
| 0–127 (Only 0–13 are used)
| The legacy Apollo NCS UUID.
|-
| 1
| 0
| x
| 128–191
| OSF DCE UUID
|-
| 1
| 1
| 0
| 192–223
| Microsoft COM / DCOM UUID
|-
| 1
| 1
| 1
| 224–255
| Reserved for future definition.
|}

The legacy Apollo NCS UUID has the format described in the previous table. The OSF DCE UUID variant is described in . The Microsoft COM / DCOM UUID has its variant described in the Microsoft documentation.

Variants

The variant field indicates the format of the UUID (and in case of the legacy UUID also the address family used for the node field). The following variants are defined:

 The Apollo NCS variant (indicated by the one-bit pattern 0xxx2) is for backwards compatibility with the now-obsolete Apollo Network Computing System 1.5 UUID format developed around 1988. Though different in detail, the similarity with modern UUIDv1 is evident. The variant bits in the current UUID specification coincide with the high bits of the address family octet in NCS UUIDs. Though the address family could hold values in the range 0..255, only the values 0..13 were ever defined. Accordingly, the bit pattern 0xxx avoids conflicts with historical NCS UUIDs, should any still exist in databases. This variant defines "families" as subtype.
 The OSF DCE variant (10xx2) are referred to as RFC 4122/DCE 1.1 UUIDs, or "Leach–Salz" UUIDs, after the authors of the original Internet Draft. This variant defines "versions" as subtype.
 The Microsoft COM/DCOM variant (110x2) is characterized in the RFC as "reserved, Microsoft Corporation backward compatibility" and was used for early GUIDs on the Microsoft Windows platform.
 The Reserved variant space is not currently used by any specification.

Versions

The OSF DCE variant defines five "versions" in the standard, and each version may be more appropriate than the others in specific use cases. The version is indicated by the value of the higher nibble (higher 4 bits, or higher hexadecimal digit) of the 7th byte of the UUID. In hex, this is the character after the second dash. For example, the UUID 9c5b94b1-35ad-49bb-b118-8e8fc24abf8 is version 4, because of the digit after the second dash is 4 in ...-49bb-....

Version 1 (date-time and MAC address)

Version 1 concatenates the 48-bit MAC address of the "node" (that is, the computer generating the UUID), with a 60-bit timestamp, being the number of 100-nanosecond intervals since midnight 15 October 1582 Coordinated Universal Time (UTC), the date on which the Gregorian calendar was first adopted outside the Catholic Church and Papal States.  RFC 4122 states that the time value rolls over around 3400 AD, depending on the algorithm used, which implies that the 60-bit timestamp is a signed quantity. However some software, such as the libuuid library, treats the timestamp as unsigned, putting the rollover time in 5623 AD. The rollover time as defined by ITU-T Rec. X.667 is 3603 AD.

A 13-bit or 14-bit "uniquifying" clock sequence extends the timestamp in order to handle cases where the processor clock does not advance fast enough, or where there are multiple processors and UUID generators per node. When UUIDs are generated faster than the system clock could advance, the lower bits of the timestamp fields can be generated by incrementing it every time a UUID is being generated, to simulate a high-resolution timestamp.  With each version 1 UUID corresponding to a single point in space (the node) and time (intervals and clock sequence), the chance of two properly generated version-1 UUIDs being unintentionally the same is practically nil.  Since the time and clock sequence total 74 bits, 274 (1.8, or 18 sextillion) version-1 UUIDs can be generated per node ID, at a maximal average rate of 163 billion per second per node ID.

In contrast to other UUID versions, version-1 and -2 UUIDs based on MAC addresses from network cards rely for their uniqueness in part on an identifier issued by a central registration authority, namely the Organizationally Unique Identifier (OUI) part of the MAC address, which is issued by the IEEE to manufacturers of networking equipment. The uniqueness of version-1 and version-2 UUIDs based on network-card MAC addresses also depends on network-card manufacturers properly assigning unique MAC addresses to their cards, which like other manufacturing processes is subject to error. Additionally some operating systems permit the end user to customise the MAC address, notably OpenWRT.

Usage of the node's network card MAC address for the node ID means that a version-1 UUID can be tracked back to the computer that created it. Documents can sometimes be traced to the computers where they were created or edited through UUIDs embedded into them by word processing software. This privacy hole was used when locating the creator of the Melissa virus.

RFC 4122 does allow the MAC address in a version-1 (or 2) UUID to be replaced by a random 48-bit node ID, either because the node does not have a MAC address, or because it is not desirable to expose it.  In that case, the RFC requires that the least significant bit of the first octet of the node ID should be set to 1. This corresponds to the multicast bit in MAC addresses, and setting it serves to differentiate UUIDs where the node ID is randomly generated from UUIDs based on MAC addresses from network cards, which typically have unicast MAC addresses.

Version 2 (date-time and MAC address, DCE security version)

RFC 4122 reserves version 2 for "DCE security" UUIDs; but it does not provide any details. For this reason, many UUID implementations omit version 2.  However, the specification of version-2 UUIDs is provided by the DCE 1.1 Authentication and Security Services specification.

Version-2 UUIDs are similar to version 1, except that the least significant 8 bits of the clock sequence are replaced by a "local domain" number, and the least significant 32 bits of the timestamp are replaced by an integer identifier meaningful within the specified local domain. On POSIX systems, local-domain numbers 0 and 1 are for user ids (UIDs) and group ids (GIDs) respectively, and other local-domain numbers are site-defined. On non-POSIX systems, all local domain numbers are site-defined.

The ability to include a 40-bit domain/identifier in the UUID comes with a tradeoff. On the one hand, 40 bits allow about 1 trillion domain/identifier values per node ID.  On the other hand, with the clock value truncated to the 28 most significant bits, compared to 60 bits in version 1, the clock in a version 2 UUID will "tick" only once every 429.49 seconds, a little more than 7 minutes, as opposed to every 100 nanoseconds for version 1.  And with a clock sequence of only 6 bits, compared to 14 bits in version 1, only 64 unique UUIDs per node/domain/identifier can be generated per 7-minute clock tick, compared to 16,384 clock sequence values for version 1. Thus, Version 2 may not be suitable for cases where UUIDs are required, per node/domain/identifier, at a rate exceeding about one every seven minutes.

Versions 3 and 5 (namespace name-based)

Version-3 and version-5 UUIDs are generated by hashing a namespace identifier and name. Version 3 uses MD5 as the hashing algorithm, and version 5 uses SHA-1.

The namespace identifier is itself a UUID. The specification provides UUIDs to represent the namespaces for URLs, fully qualified domain names, object identifiers, and X.500 distinguished names; but any desired UUID may be used as a namespace designator.

To determine the version-3 UUID corresponding to a given namespace and name, the UUID of the namespace is transformed to a string of bytes, concatenated with the input name, then hashed with MD5, yielding 128 bits.  Then 6 or 7 bits are replaced by fixed values, the 4-bit version (e.g. 00112 for version 3), and the 2- or 3-bit UUID "variant" (e.g. 102 indicating a RFC 4122 UUIDs, or 1102 indicating a legacy Microsoft GUID). Since 6 or 7 bits are thus predetermined, only 121 or 122 bits contribute to the uniqueness of the UUID.

Version-5 UUIDs are similar, but SHA-1 is used instead of MD5. Since SHA-1 generates 160-bit digests, the digest is truncated to 128 bits before the version and variant bits are replaced.

Version-3 and version-5 UUIDs have the property that the same namespace and name will map to the same UUID. However, neither the namespace nor name can be determined from the UUID, even if one of them is specified, except by brute-force search. RFC 4122 recommends version 5 (SHA-1) over version 3 (MD5), and warns against use of UUIDs of either version as security credentials.

Version 4 (random)

A version 4 UUID is randomly generated.  As in other UUIDs, 4 bits are used to indicate version 4, and 2 or 3 bits to indicate the variant (102 or 1102 for variants 1 and 2 respectively). Thus, for variant 1 (that is, most UUIDs) a random version-4 UUID will have 6 predetermined variant and version bits, leaving 122 bits for the randomly generated part, for a total of 2122, or 5.3 (5.3 undecillion) possible version-4 variant-1 UUIDs.  There are half as many possible version-4 variant-2 UUIDs (legacy GUIDs) because there is one less random bit available, 3 bits being consumed for the variant.

Special UUIDs

The "nil" UUID, a special case, is the UUID 00000000-0000-0000-0000-000000000000; that is, all bits set to zero.

The "Max" UUID, a special case, is the UUID FFFFFFFF-FFFF-FFFF-FFFF-FFFFFFFFFFFF; that is, all bits set to one.

Textual representation

Because a UUID is a 128 bit label, it can be represented in different formats.

In most cases, UUIDs are represented as hexadecimal values. The most used format is the 8-4-4-4-12 format, xxxxxxxx-xxxx-xxxx-xxxx-xxxxxxxxxxxx, where every x represents 4 bits. Other well-known formats are the 8-4-4-4-12 format with braces, {xxxxxxxx-xxxx-xxxx-xxxx-xxxxxxxxxxxx}, like in Microsoft's systems, e.g. Windows, or xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx, where all hyphens are removed. In some cases, it is also possible to have xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx with the "0x" prefix or the "h" suffix to indicate hexadecimal values. The format with hyphens was introduced with the newer variant system. Before that, the legacy Apollo format used a slightly different format: 34dc23469000.0d.00.00.7c.5f.00.00.00. The first part is the time (time_high and time_low combined). The reserved field is skipped. The family field comes directly after the first dot, so in this case 0d (13 in decimal) for DDS (Data Distribution Service). The remaining parts, each separated with a dot, are the node bytes.

A UUID can be represented as a 128 bit integer. For example, the UUID 550e8400-e29b-41d4-a716-446655440000 can also be represented as 113059749145936325402354257176981405696. Note that it is possible to have both signed and unsigned values if the first bit of the UUID is set to 1.

A UUID can be represented as a  128 bit binary number. For example, the UUID 550e8400-e29b-41d4-a716-446655440000 can also be represented as 01010101000011101000010000000000111000101001101101000001110101001010011100010110010001000110011001010101010001000000000000000000.

 registered the "uuid" namespace. This makes it possible to make URNs out of UUIDs, like urn:uuid:550e8400-e29b-41d4-a716-446655440000. The normal 8-4-4-4-12 format is used for this. It is also possible to make a OID URN out of UUIDs, like urn:oid:2.25.113059749145936325402354257176981405696. In that case, the unsigned decimal format is used. The "uuid" URN is recommended over the "oid" URN.

Encoding

The binary encoding of UUIDs varies between systems. Variant 1 UUIDs, nowadays the most common variant, are encoded in a big-endian format. For example, 00112233-4455-6677-8899-aabbccddeeff is encoded as the bytes 00 11 22 33 44 55 66 77 88 99 aa bb cc dd ee ff.

Variant 2 UUIDs, historically used in Microsoft's COM/OLE libraries, use a little-endian format, but appear mixed-endian with the first three components of the UUID as little-endian and last two big-endian, due to the missing byte dashes when formatted as a string. For example, 00112233-4455-6677-8899-aabbccddeeff is encoded as the bytes 33 22 11 00 55 44 77 66 88 99 aa bb cc dd ee ff.

Collisions

Collision occurs when the same UUID is generated more than once and assigned to different referents. In the case of standard version-1 and version-2 UUIDs using unique MAC addresses from network cards, collisions are unlikely to occur, with an increased possibility only when an implementation varies from the standards, either inadvertently or intentionally.

In contrast to version-1 and version-2 UUIDs generated using MAC addresses, with version-1 and -2 UUIDs which use randomly generated node ids, hash-based version-3 and version-5 UUIDs, and random version-4 UUIDs, collisions can occur even without implementation problems, albeit with a probability so small that it can normally be ignored. This probability can be computed precisely based on analysis of the birthday problem.

For example, the number of random version-4 UUIDs which need to be generated in order to have a 50% probability of at least one collision is 2.71 quintillion, computed as follows:

This number is equivalent to generating 1 billion UUIDs per second for about 86 years. A file containing this many UUIDs, at 16 bytes per UUID, would be about 45 exabytes.

The smallest number of version-4 UUIDs which must be generated for the probability of finding a collision to be p is approximated by the formula

Thus, the probability to find a duplicate within 103 trillion version-4 UUIDs is one in a billion.

Uses

Significant uses include ext2/ext3/ext4 filesystem userspace tools (e2fsprogs uses libuuid provided by util-linux), LVM, LUKS encrypted partitions, GNOME, KDE, and macOS, most of which are derived from the original implementation by Theodore Ts'o. One of the uses of UUIDs in Solaris (using Open Software Foundation implementation) is identification of a running operating system instance for the purpose of pairing crash dump data with Fault Management Event in the case of kernel panic. The "partition label" and the "partition UUID" are both stored in the superblock. They are both part of the file system rather than of the partition. For example, ext2–4 contain a UUID, while NTFS or FAT32 do not. The superblock is a part of the file system, thus fully contained within the partition, hence doing  leaves both sda1 and sdb1 with the same label and UUID.

There are several flavors of GUIDs used in Microsoft's Component Object Model (COM):

  – interface identifier; (The ones that are registered on a system are stored in the Windows Registry at  )
   – class identifier; (Stored at )
  – type library identifier; (Stored at )
  – category identifier; (its presence on a class identifies it as belonging to certain class categories, listed at )

UUIDs are commonly used as a unique key in database tables. The  function in Microsoft SQL Server version 4 Transact-SQL returns standard random version-4 UUIDs, while the  function returns 128-bit identifiers similar to UUIDs which are committed to ascend in sequence until the next system reboot. The Oracle Database  function does not return a standard GUID, despite the name.  Instead, it returns a 16-byte 128-bit RAW value based on a host identifier and a process or thread identifier, somewhat similar to a GUID. PostgreSQL contains a  datatype and can generate most versions of UUIDs through the use of functions from modules. MySQL provides a  function, which generates standard version-1 UUIDs. The random nature of standard UUIDs of versions 3, 4, and 5, and the ordering of the fields within standard versions 1 and 2 may create problems with database locality or performance when UUIDs are used as primary keys. For example, in 2002 Jimmy Nilsson reported a significant improvement in performance with Microsoft SQL Server when the version-4 UUIDs being used as keys were modified to include a non-random suffix based on system time. This so-called "COMB" (combined time-GUID) approach made the UUIDs non-standard and significantly more likely to be duplicated, as Nilsson acknowledged, but Nilsson only required uniqueness within the application. By reordering and encoding version 1 and 2 UUIDs so that the timestamp comes first, insertion performance loss can be averted.

Some web frameworks, such as Laravel, have support for "timestamp first" UUIDs that may be efficiently stored in an indexed database column. This makes a COMB UUID using version 4 format, but where the first 48-bits make up a timestamp laid out like in UUIDv1. More specified formats based on the COMB UUID idea include:

 "ULID", which ditches the 4 bits used to indicate version 4, and uses a base32 encoding by default.
 UUID versions 6 through 8, a formal proposal of three COMB UUID formats.

See also

 Birthday attack
 Object identifier (OID)
 Uniform Resource Identifier (URI)
 Snowflake ID

References

External links

 Recommendation ITU-T X.667 (Free access)
 ISO/IEC 9834-8:2014 (Paid)
 Technical Note TN2166 - Secrets of the GPT - Apple Developer
 UUID Documentation - Apache Commons Id
 CLSID Key - Microsoft Docs
 Universal Unique Identifier - The Open Group Library
 UUID Decoder tool
 A Brief History of the UUID
 Understanding How UUIDs Are Generated

Unique identifiers
Windows administration
1996 establishments

Universally unique identifier


A pizza party is a social gathering at which pizza is served.

Typically, a pizza that is 10 to 14 inches wide will feed two people.  Since pizzas can include a very wide variety of toppings, one particular type of pizza party allows the guests to create their own custom-made pizza, using a selection of ingredients from among the toppings provided by the party's host.

When a pizza party does not include any custom-made pizzas, and the particular preferences of the guests are unknown, it is common to include at least one plain cheese-only and/or vegetable-only pizza for people who are averse to meats or other available toppings.

Notable pizza parties

On September 8, 2019, one of the largest pizza parties was held at the Ippodromo Capannelle in Rome, where 1,146 people dined on pizza together.

On September 18, 2020, Hormel Foods hosted the world's then largest virtual pizza party, when more than 3,000 people joined a Zoom-hosted pizza party. In order to break the record, at least 500 photos of individuals needed to be uploaded during the one-hour event. The final tally was 907 photos.

In August 2021, astronauts aboard the International Space Station held the very first pizza party in space, following a cargo shipment that included pizza-making ingredients.

See also
Grated cheese

References

Pizza
Parties

Pizza party


Carlo Sellitto (1581 – 2 October 1614 in Naples) was an Italian painter of the Baroque period.

One of the most gifted followers of Michelangelo Merisi da Caravaggio (1571–1610), Sellitto played an important role in the spread of Caravaggism to Naples and in the development away from Late Mannerism to a greater naturalism.

The son of a painter and gilder, he was apprenticed briefly to the Piedmontese painter Giovanni Antonio Ardito (c. late 16th century–early 17th) before moving (c. 1591) to the studio of the Flemish painter Louis Croys. By 1608, at the age of 27 years, he had left Croys and had set up his own workshop in the Via Donnalbina, attracting to it such artists as Filippo Napoletano, Giovan Mattea Arciero (b 1591) and Francesco Abbenante (first decade of the 17th century). The talent for portraiture that Sellitto had shown while working with Croys brought him commissions from the court and aristocracy, although none of these documented works has been identified.

Sellitto would have known Caravaggio during the artist's exile in Naples in 1606/1607, but the date indicates that this Baptist (illustrated) was painted several years previously - cf. Caravaggio's own treatment of the theme of John the Baptist.

He died on 2 October 1614 after a brief 6-year independent career.

External links

Paintings by Sellitto at Montemurro Sul Web

1581 births
1614 deaths
Italian Baroque painters
16th-century Italian painters
Italian male painters
17th-century Italian painters
Painters from Naples
Caravaggisti

Carlo Sellitto


The 2011 Italian Census is the fifteenth and most recent Italian national census. The reference day used for the census was October 9, 2011. The population was counted at 59,433,744.

A census of the whole population has taken place in Italy every 10 years since 1861.

References

Censuses in Italy
Census
Italy

2011 Italian census


In racket sports a groundstroke, or ground stroke, refers to a forehand or backhand shot that is executed after the ball has bounced on the court. The term is commonly used in the sports of tennis and pickleball, and is counter to a volley shot which is taken before the ball has bounced. Groundstrokes in tennis are usually hit from the back of the court, around the baseline.

There are many factors that may define a good groundstroke. For example, one groundstroke may use topspin and another backspin. Both can be effective for different reasons having to do with depth, opponent's strength or weaknesses, etc. Some characteristics of groundstrokes are: depth (how close the ball lands to the opponent's baseline), consistency (the tendency of groundstrokes to not drop short or into an opponent's strike range in rallies with many groundstrokes), speed (how fast it travels in the air), pace (the ball's behavior after it bounces on the opponent's side), trajectory and angle. If a "good groundstroke" is to be played, it would generally have a combination of the above characteristics to produce a shot that is difficult for the opponent to return. Generally, a groundstroke that lands deep and in the corner of the opponent's court will make it more difficult for the opponent to return the ball. However, this is somewhat arbitrary and depends on the opponent and stage of the point being played. For example, a short angled shot, a moon ball (very high trajectory), an off pace shot, etc., may prove effective against opponent A but not opponent B.

In tennis, a player whose strategy is to trade groundstrokes with the opponent is termed a baseliner, as opposed to volleyers who prefer to hit volleys near the net.

Players with great groundstrokes

 Jimmy Connors
 Björn Borg
 Ivan Lendl
 Andre Agassi
 Marcelo Ríos
 Gustavo Kuerten
 Yevgeny Kafelnikov
 Marat Safin
 David Nalbandian
 Nikolay Davydenko
 Novak Djokovic
 Kei Nishikori
 Marin Čilić
 Jannik Sinner

 Chris Evert
 Monica Seles
 Mary Pierce
 Lindsay Davenport
 Serena Williams
 Justine Henin
 Kim Clijsters
 Na Li
 Maria Sharapova
 Victoria Azarenka
 Petra Kvitová
 Anastasia Pavlyuchenkova
 Karolína Plíšková
 Iga Świątek

See also

 Glossary of tennis terms
 Glossary of pickleball terms
 Tennis shots
 Serve
 Volley
 Smash

References

Sources
 Tennis 101: The 6 Basic Strokes Explained

Tennis shots
Pickleball terminology

Groundstroke


Janice Murray (born 26 October 1966) is an English former international footballer. She played as a left winger for clubs including Leasowe Pacific, Doncaster Belles and Liverpool Ladies. Murray won around thirty caps for the senior England women's national football team.

Club career
Murray acquired the nickname Psycho. During a match on her native Merseyside, she scored a free kick in a manner which a spectator likened to Zico. The comment, made in scouse, was misheard as Psycho and the name remained with Murray throughout her career. In April 1993 football journalist Henry Winter wrote in The Independent that Murray was "nicknamed 'Psycho' but the possessor of skills more Finney than Vinnie."

She helped Leasowe win the 1989 WFA Cup then won two doubles with Doncaster Belles in 1992 and 1994. Murray returned to Merseyside with newly formed Liverpool Ladies in 1994.

International career
On 23 May 1989, 22-year-old Murray made a debut England appearance in a 2–0 home friendly defeat by Sweden. The match was held at Wembley Stadium to mark the 20th anniversary of the Women's Football Association (WFA) and was played as a curtain raiser to the male national team's Rous Cup game against Chile.

When The Football Association (FA) took over running the national team in 1993, Murray started the first game that September, a 10–0 win over Slovenia in Ljubljana. Manager Ted Copeland selected Murray in the next three 1995 UEFA Women's Championship qualifiers, before she retired from international duty along with club teammate Tracey Davidson. Davidson remarked that: "The management leave a lot to be desired, and if you don't enjoy it, what's the point?"

Murray's subsequent absence from England's 1995 FIFA Women's World Cup squad was controversial. Doncaster Belles manager Paul Edmunds described it as a disaster for the team: "It's such a shame she's not going to Sweden. She'd go down the line, she'd pop in the cross, Kaz'd score on the end of it – she'd solve his [Copeland's] left-side problem in one go. But he's put her off, hasn't he? Disaster, that."

She was allotted 77 when the FA announced their legacy numbers scheme to honour the 50th anniversary of England's inaugural international.

References

General references

1966 births
Living people
English women's footballers
Everton F.C. (women) players
Doncaster Rovers Belles L.F.C. players
Liverpool F.C. Women players
England women's international footballers
FA Women's National League players
Women's association football wingers
Footballers from Birkenhead

Janice Murray (footballer)


José María Lanz y Zaldívar (March 26, 1764 – 1839) was a Spanish-Mexican mathematician and engineer. Together with Agustín de Betancourt, he developed the classification of mechanisms begun by Jean Nicolas Pierre Hachette, and counts as one of the founders of industrial kinematics (machine construction).

His name is sometimes written as Philippe Louis Lanz.

Biography
He was born in Campeche in the south-east of Mexico, then Viceroyalty of New_Spain, and studied at Instituto Campechano, where he was later also a teacher. He continued to study naval engineering in Spain. In 1781 he joined the Spanish Royal Navy at Cadiz, working as a cartographer and lecturer in mathematics. In Yucatan he studied the use of henequen for making ropes and other naval utensils, and published a report on this in 1783, making him the first to write about the use of this plant. In 1789 he made a tour through Europe with Josef de Mendoza y Ríos, visiting France, England, Germany, Sweden, Poland and Russia. In Paris he met Gaspard Monge and Agustín de Betancourt. Lanz left the navy in 1792, stayed in Paris and married there.

When Betancourt in 1802 founded the Engineering School for Roads, Canals and Harbours (Escuela de Ingenieros de Caminos, Canales y Puertos), today a branch of the Technical University of Madrid, Lanz became a professor there, and remained so until 1805.

Soon after the establishment in 1794 of École Polytechnique in Paris, Monge had proposed a class on the analysis of mechanisms and described the subject to fellow teachers. When the class was first taught in 1806 by Hachette, Lanz and Betancourt were among its students. Lanz revised his lecture notes and published them together with Betancourt as Essai sur la composition des machines (1808; 2nd ed. 1819; 3rd ed. 1840), encouraged to do so by Monge and Hachette. This textbook on machine design became widespread in European universities. It was translated to English as Analytical essay of the construction of machines (1820, published by Rudolph Ackermann) and by Thomas Fenwick as Essays on practical mechanics (1822) and to German by Wilhelm Kreyher as Versuch über die Zusammensetzung der Maschinen (1829).

In the years 1805–1808, he led a Commission for science and art and 1808–1812 he worked for the ministry of the interior. In 1812 he went in exile to South America, and in 1816 became director for a school of mathematics in Buenos Aires. From 1817 he worked in Paris as a translator and private instructor. Between 1822 and 1826, he worked for the military of the recently independent republic of Gran Colombia as a cartographer, founder of schools, founder of a museum, and director of an observatory. Back in Paris, he lectured at a school of geography and collaborated with watchmaker Breguet. He died in 1839 in Paris.

References
Lanz, José Maria de, presented in German by "Digitale Mechanismen- und Getriebebibliothek"
"José María Lanz y Zaldívar (1764-1839)", chapter by Carlos S. López Cajún in Distinguished Figures in Mechanism and Machine Science, (2010), pages 111-121; this is volume 7 of the series "History of mechanism and machine science", Springer Verlag, information from the publisher,

External links
The German "Digitale Mechanismen- und Getriebebibliothek" has digitized:
Essai sur la composition des machines (2nd ed. 1819)  metadata, fulltext viewer
Versuch über die Zusammensetzung der Maschinen (1829) metadata, fulltext viewer

Spanish engineers
Mexican engineers
1764 births
1839 deaths
People from Campeche City

José María Lanz


Francesca Isabel Natividad (February 13, 1948 – September 24, 2022), known professionally as Kitten Natividad, was a Mexican-American film actress and exotic dancer. She was noted for her 44-inch (112 cm) bust, and appearances in cult films made by her ex-partner, director Russ Meyer.

Early years
Natividad was born on February 13, 1948, in Ciudad Juárez, Chihuahua State, Mexico. She was the eldest of nine children. Natividad did not speak English until she was 10 years old. At that time, her mother married a U.S. citizen and they moved to Texas. Natividad attended Ysleta High School in El Paso, where she was her senior class president.

After moving to California, Natividad worked as both a maid and a cook for Stella Stevens, and then as a key-punch operator for IBM, before eventually turning to go-go dancing to make ends meet. At this time, she adopted the stage name of "Kitten" Natividad, which came from her shyness. In 1969, at the age of 21 years, she had her first breast implant surgery in Tijuana (where it was legal) on the advice of her agent.

Career
Natividad, by then known mainly as Kitten, was introduced to Russ Meyer by fellow dancer Shari Eubank, a performer in Meyer's 1975 film Supervixens. Meyer hired her to narrate his movie Up! In it, she was shown sitting nude in a tree, quoting the poetry of H.D., and acting as a Greek chorus to the nonsensical action. Meyer was so impressed he wanted her to star in his next feature, Beneath the Valley of the Ultra-Vixens, one of several collaborations between Meyer and film critic Roger Ebert. Meyer paid for a second breast enhancement and voice lessons to eliminate her accent. Due to the tragic results of her breast enhancement surgeries she deeply regretted what she was talked into doing. She left her husband for Meyer during the filming, and they lived together as a couple for most of the next 15 years.

After this, Natividad moved into pornographic modeling, mainly doing glamour or girl-girl shoots with the likes of Candy Samples, Uschi Digard, and Patty Plenty. The appearances increased her dancing income many times over. She incorporated a giant champagne glass into her act, similar to such as Lili St. Cyr had used, accompanied by the Bobby Darin hit "Splish Splash". She appeared as a guest on The Dating Game, one of a number of game shows that Chuck Barris produced.

During the 1980s, Natividad began appearing in pornographic productions, initially limiting her performances to appearing topless. Eventually, however, she graduated to engaging in hardcore performances, usually with younger men and women. She has had backlash from burlesque performers because she did hardcore videos. She also founded the private photo and video studio called "The Kitten Klub". Her website later closed. She famously appeared as a stripper at the bachelor party held by Sean Penn to celebrate his 1985 marriage to Madonna, having portrayed a stripper the year before in The Wild Life, a movie starring Sean's brother Christopher.

In 2001, Natividad starred in the cult film comedy The Double-D Avenger, directed by William Winckler, and in it, she was reunited with fellow Russ Meyer "repertory" stars Haji (from Meyer's Faster Pussycat! Kill! Kill!) and Raven De La Croix from Meyer's film Up! In The Double-D Avenger, Kitten Natividad played Chastity Knott, a woman who becomes a busty costumed crime fighter.
The pornographic website Brazzers was negotiating her return to hardcore performances.

In pop culture
 Natividad appeared on The Gong Show in the late 1970s and on The $1.98 Beauty Show, both of which, like The Dating Game, were produced by Chuck Barris. (Barris hosted The Gong Show; Rip Taylor hosted The $1.98 Beauty Show; and Jim Lange hosted The Dating Game.)
 She appeared in a 1980s music video for Mitch Ryder's version of the song "When You Were Mine", which was written and composed by Prince.
 In August 2006, Natividad appeared in a Playboy layout, "The History of Bikinis".

Personal life
In October 1999, Natividad underwent double-mastectomy surgery for treatment of breast cancer. After her breasts were removed, it was discovered that the silicone that had been used in her implants when she had undergone her 1969 surgery was of an industrial grade rather than a surgical grade. She subsequently underwent corrective surgery, and this brought her closer to the size that her fans remembered her having been.

As of early August 2016, she was living alone with a pit bull and three cats, all of which were featured in the 2005 documentary movie Pornstar Pets, and she continued to support herself with sales of her porn videos and phone sex. She appeared in the Adam Rifkin independent feature A Night at the Golden Eagle; according to her, Rifkin remembered recognizing her when their cars were both stopped at the same stoplight 25 years earlier.

Death
Natividad died from kidney failure at Cedars Sinai Hospital in Los Angeles on September 24, 2022, aged 74. She was survived by her sister Eva, her mother, four nephews and a niece.

Selected filmography
Kitten Natividad has appeared in more than 65 films and video productions. Career highlights and major studio features include:

 1972: The New Centurions
 1976: Up!
 1979: Beneath the Valley of the Ultra-Vixens
 1976: Deep Jaws
 1980: Airplane! (uncredited)
 1982: Airplane II: The Sequel (uncredited)
 1982: The Best Little Whorehouse in Texas (uncredited)
 1983: My Tutor
 1984: Night Patrol
 1984: The Wild Life
 1985: Takin' It Off
 1985: Bodacious Ta Tas
 1985: An Evening with Kitten
 1986: The Tomb
 1987: Takin' It All Off
 1990: Another 48 Hrs.
 1990: 40 The Hard Way
 1993: Titillation 3
 1993: Buford's Beach Bunnies
 1996: United Trash
 1997: The 120 Days of Bottrop
 2001: The Double-D Avenger
 2001: Night at the Golden Eagle
 2009: Nightbeats
 2017: Fags in the Fast Lane
 2019: 70 the Hard Way

References

External links

 Official site

1948 births
2022 deaths
American female erotic dancers
American erotic dancers
American female adult models
American pornographic film actresses
American film actresses
Mexican emigrants to the United States
American burlesque performers
American vedettes
Hispanic and Latino American female models
Hispanic and Latino American pornographic film actors
Mexican female adult models
Mexican erotic dancers
Mexican pornographic film actresses
Mexican film actresses
People from Ciudad Juárez
20th-century Mexican dancers
21st-century Mexican dancers
20th-century Mexican actresses
21st-century Mexican actresses
20th-century American dancers
21st-century American dancers
20th-century American actresses
21st-century American actresses

Kitten Natividad