Linear regression
In statistics, linear regression is a linear approach to modelling the relationship between a scalar response and one or more explanatory variables. The case of one explanatory variable is called simple linear regression. For more than one explanatory variable, the process is called multiple linear regression; this term is distinct from multivariate linear regression, where multiple correlated dependent variables are predicted, rather than a single scalar variable. In linear regression, the relationships are modeled using linear predictor functions whose unknown model parameters are estimated from the data; such models are called linear models. Most the conditional mean of the response given the values of the explanatory variables is assumed to be an affine function of those values. Like all forms of regression analysis, linear regression focuses on the conditional probability distribution of the response given the values of the predictors, rather than on the joint probability distribution of all of these variables, the domain of multivariate analysis.
Linear regression was the first type of regression analysis to be studied rigorously, to be used extensively in practical applications. This is because models which depend linearly on their unknown parameters are easier to fit than models which are non-linearly related to their parameters and because the statistical properties of the resulting estimators are easier to determine. Linear regression has many practical uses. Most applications fall into one of the following two broad categories: If the goal is prediction, or forecasting, or error reduction, linear regression can be used to fit a predictive model to an observed data set of values of the response and explanatory variables. After developing such a model, if additional values of the explanatory variables are collected without an accompanying response value, the fitted model can be used to make a prediction of the response. If the goal is to explain variation in the response variable that can be attributed to variation in the explanatory variables, linear regression analysis can be applied to quantify the strength of the relationship between the response and the explanatory variables, in particular to determine whether some explanatory variables may have no linear relationship with the response at all, or to identify which subsets of explanatory variables may contain redundant information about the response.
Linear regression models are fitted using the least squares approach, but they may be fitted in other ways, such as by minimizing the "lack of fit" in some other norm, or by minimizing a penalized version of the least squares cost function as in ridge regression and lasso. Conversely, the least squares approach can be used to fit models. Thus, although the terms "least squares" and "linear model" are linked, they are not synonymous. Given a data set i = 1 n of n statistical units, a linear regression model assumes that the relationship between the dependent variable y and the p-vector of regressors x is linear; this relationship is modeled through a disturbance term or error variable ε — an unobserved random variable that adds "noise" to the linear relationship between the dependent variable and regressors. Thus the model takes the form y i = β 0 1 + β 1 x i 1 + ⋯ + β p x i p + ε i = x i T β + ε i, i = 1, …, n, where T denotes the transpose, so that xiTβ is the inner product between vectors xi and β.
These n equations are stacked together and written in matrix notation as y = X β + ε, where y =, X = = ( 1 x 11 ⋯ x 1 p 1 x 21 ⋯ x 2 p ⋮ ⋮ ⋱ ⋮ 1 x n
Hill equation (biochemistry)
In biochemistry and pharmacology, the Hill equation refers to two related equations that reflect ligands binding to macromolecule. The distinction between the two equations is whether they measure response. Both equations are a function of the ligand concentration; as the Hill equation is formally equivalent to the Langmuir isotherm, it is sometimes referred to as the Hill-Langmuir equation. The International Union of Basic and Clinical Pharmacology has proposed to cement this subtle distinction and define separately the Hill-Langmuir equation, which reflects occupancy of receptors by ligands, the Hill equation, which reflects response to the ligand; this article will use the IUPHAR convention. A slight, yet subtle, distinction is made between the Hill-Langmuir equation, which reflects occupancy of receptors by ligands, the Hill equation, which reflects response to the ligand; the Hill-Langmuir equation was formulated by Archibald Hill in 1910 to describe the sigmoidal O2 binding curve of haemoglobin.
The binding of a ligand to a macromolecule is enhanced if there are other ligands present on the same macromolecule. The Hill-Langmuir equation is useful for determining the degree of cooperativity of the ligand binding to the enzyme or receptor; the Hill coefficient provides a way to quantify the degree of interaction between ligand binding sites. The Hill equation is important in the construction of dose-response curves; the Hill-Langmuir equation is a special case of a Rectangular hyperbola and is expressed in the following ways: θ = n K d + n = n n + n = 1 1 + n,where: θ is the fraction of the receptor protein concentration, bound by the ligand, is the free, unbound ligand concentration, K d is the apparent dissociation constant derived from the law of mass action, K A is the ligand concentration producing half occupation, n is the Hill coefficient. In pharmacology, θ is written as p A R, where A is the ligand, equivalent to L, R is the receptor. Θ can be expressed in terms of the total amount of receptor and ligand-bound receptor concentrations: θ =.
K d is equal to the ratio of the dissociation rate of the ligand-receptor complex to its association rate. Kd is the equilibrium constant for dissociation. K A is defined so that n = K d = k d k a, this is known as the microscopic dissociation constant and is the ligand concentration occupying half of the binding sites. In recent literature, this constant is sometimes referred to as K D; the Gaddum equation is a further generalisation of the Hill-equation, incorporating the presence of a reversible competitive antagonist. The Gaddum equation is derived to the Hill-equation but with 2 equilibria: both the ligand with the receptor and the antagonist with the receptor. Hence, the Gaddum equation has 2 constants: the equilibrium constants of the ligand and that of the antagonist The Hill plot is the rearrangement of the Hill-Langmuir Equation into a straight line. Taking the reciprocal of both sides of the Hill-Langmuir equation and inverting again yields
Drug
A drug is any substance that, when inhaled, smoked, absorbed via a patch on the skin, or dissolved under the tongue causes a physiological change in the body. In pharmacology, a drug is a chemical substance of known structure, other than a nutrient of an essential dietary ingredient, when administered to a living organism, produces a biological effect. A pharmaceutical drug called a medication or medicine, is a chemical substance used to treat, prevent, or diagnose a disease or to promote well-being. Traditionally drugs were obtained through extraction from medicinal plants, but more also by organic synthesis. Pharmaceutical drugs may be used for a limited duration, or on a regular basis for chronic disorders. Pharmaceutical drugs are classified into drug classes—groups of related drugs that have similar chemical structures, the same mechanism of action, a related mode of action, that are used to treat the same disease; the Anatomical Therapeutic Chemical Classification System, the most used drug classification system, assigns drugs a unique ATC code, an alphanumeric code that assigns it to specific drug classes within the ATC system.
Another major classification system is the Biopharmaceutics Classification System. This classifies drugs according to their permeability or absorption properties. Psychoactive drugs are chemical substances that affect the function of the central nervous system, altering perception, mood or consciousness, they include alcohol, a depressant, the stimulants nicotine and caffeine. These three are the most consumed psychoactive drugs worldwide and are considered recreational drugs since they are used for pleasure rather than medicinal purposes. Other recreational drugs include hallucinogens and amphetamines and some of these are used in spiritual or religious settings; some drugs can cause addiction and all drugs can have side effects. Excessive use of stimulants can promote stimulant psychosis. Many recreational drugs are illicit and international treaties such as the Single Convention on Narcotic Drugs exist for the purpose of their prohibition. In English, the noun "drug" is thought to originate from Old French "drogue" deriving into "droge-vate" from Middle Dutch meaning "dry barrels", referring to medicinal plants preserved in them.
The transitive verb "to drug" arose and invokes the psychoactive rather than medicinal properties of a substance. A medication or medicine is a drug taken to cure or ameliorate any symptoms of an illness or medical condition; the use may be as preventive medicine that has future benefits but does not treat any existing or pre-existing diseases or symptoms. Dispensing of medication is regulated by governments into three categories—over-the-counter medications, which are available in pharmacies and supermarkets without special restrictions. In the United Kingdom, behind-the-counter medicines are called pharmacy medicines which can only be sold in registered pharmacies, by or under the supervision of a pharmacist; these medications are designated by the letter P on the label. The range of medicines available without a prescription varies from country to country. Medications are produced by pharmaceutical companies and are patented to give the developer exclusive rights to produce them; those that are not patented are called generic drugs since they can be produced by other companies without restrictions or licenses from the patent holder.
Pharmaceutical drugs are categorised into drug classes. A group of drugs will share a similar chemical structure, or have the same mechanism of action, the same related mode of action or target the same illness or related illnesses; the Anatomical Therapeutic Chemical Classification System, the most used drug classification system, assigns drugs a unique ATC code, an alphanumeric code that assigns it to specific drug classes within the ATC system. Another major classification system is the Biopharmaceutics Classification System; this groups drugs according to their permeability or absorption properties. Some religions ethnic religions are based on the use of certain drugs, known as entheogens, which are hallucinogens,—psychedelics, dissociatives, or deliriants; some drugs used as entheogens include kava which can act as a stimulant, a sedative, a euphoriant and an anesthetic. The roots of the kava plant are used to produce a drink, consumed throughout the cultures of the Pacific Ocean; some shamans from different cultures use entheogens, defined as "generating the divine within" to achieve religious ecstasy.
Amazonian shamans use ayahuasca a hallucinogenic brew for this purpose. Mazatec shamans have a long and continuous tradition of religious use of Salvia divinorum a psychoactive plant, its use is to facilitate visionary states of consciousness during spiritual healing sessions. Silene undulata is used as an entheogen, its root is traditionally used to induce vivid lucid dreams during the initiation process of shamans, classifying it a occurring oneirogen similar to the more well-known dream herb Calea ternifolia. Peyote a small spineless cactus has been a
Logistic function
A logistic function or logistic curve is a common "S" shape, with equation: f = L 1 + e − k where e = the natural logarithm base, x0 = the x-value of the sigmoid's midpoint, L = the curve's maximum value, k = the logistic growth rate or steepness of the curve. For values of x in the domain of real numbers from −∞ to +∞, the S-curve shown on the right is obtained, with the graph of f approaching L as x approaches +∞ and approaching zero as x approaches −∞; the logistic function finds applications in a range of fields, including artificial neural networks, biomathematics, demography, geoscience, mathematical psychology, sociology, political science and statistics. The function was named in 1844 by Pierre François Verhulst, who studied it in relation to population growth; the initial stage of growth is exponential. Verhulst did not explain the choice of the term "logistic", but it is in contrast to the logarithmic curve, by analogy with arithmetic and geometric, his growth model is preceded by a discussion of arithmetic growth and geometric growth, thus "logistic growth" is named by analogy, logistic being from Ancient Greek: λογῐστῐκός, translit.
Logistikós, a traditional division of Greek mathematics. The term is unrelated to the military and management term logistics, instead from French: logis "lodgings", though some believe the Greek term influenced logistics; the standard logistic function is the logistic function with parameters which yields f = 1 1 + e − x = e x e x + 1 = 1 2 + 1 2 tanh In practice, due to the nature of the exponential function e−x, it is sufficient to compute the standard logistic function for x over a small range of real numbers such as a range contained in as it converges close to its saturation values of 0 and 1. The logistic function has the symmetry property that: 1 − f = f. Thus, x ↦ f − 1 / 2 is an odd function; the logistic function is an offset and scaled hyperbolic tangent function f = 1 2 + 1 2 tanh or tanh = 2 f − 1. This follows from tanh = e x − e − x e x + e − x = e x ⋅ e x ⋅ = f − e − 2 x 1 + e − 2 x = f − e − 2
Wiley (publisher)
John Wiley & Sons, Inc. branded as Wiley in recent years, is a global publishing company that specializes in academic publishing and instructional materials. The company produces books and encyclopedias, in print and electronically, as well as online products and services, training materials, educational materials for undergraduate and continuing education students. Founded in 1807, Wiley is known for publishing the For Dummies book series. In 2017, the company had a revenue of $1.7 billion. Wiley was established in 1807; the company was the publisher of such 19th century American literary figures as James Fenimore Cooper, Washington Irving, Herman Melville, Edgar Allan Poe, as well as of legal and other non-fiction titles. Wiley worked in partnership with Cornelius Van Winkle, George Long, George Palmer Putnam, Robert Halsted; the firm took its current name in 1865. Wiley shifted its focus to scientific and engineering subject areas, abandoning its literary interests. Charles Wiley's son John took over the business when his father died in 1826.
The firm was successively named Wiley, Lane & Co. Wiley & Putnam, John Wiley; the company acquired its present name in 1876, when John's second son William H. Wiley joined his brother Charles in the business. Through the 20th century, the company expanded its publishing activities, the sciences, higher education. Since the establishment of the Nobel Prize in 1901, Wiley and its acquired companies have published the works of more than 450 Nobel Laureates, in every category in which the prize is awarded. One of the world's oldest independent publishing companies, Wiley marked its bicentennial in 2007 with a year-long celebration, hosting festivities that spanned four continents and ten countries and included such highlights as ringing the closing bell at the New York Stock Exchange on May 1. In conjunction with the anniversary, the company published Knowledge for Generations: Wiley and the Global Publishing Industry, 1807-2007, depicting Wiley's pivotal role in the evolution of publishing against a social and economic backdrop.
Wiley has created an online community called Wiley Living History, offering excerpts from Knowledge for Generations and a forum for visitors and Wiley employees to post their comments and anecdotes. In December 2010, Wiley opened an office in Dubai; the company has had an office in Beijing, since 2001, China is now its sixth-largest market for STEM content. Wiley established publishing operations in India in 2006, has established a presence in North Africa through sales contracts with academic institutions in Tunisia and Egypt. On April 16, 2012, the company announced the establishment of Wiley Brasil Editora LTDA in São Paulo, effective May 1, 2012. Wiley's scientific and medical business was expanded by the acquisition of Blackwell Publishing in February 2007; the combined business, named Scientific, Technical and Scholarly, publishes, in print and online, 1,400 scholarly peer-reviewed journals and an extensive collection of books, major reference works and laboratory manuals in the life and physical sciences and allied health, the humanities, the social sciences.
Through a backfile initiative completed in 2007, 8.2 million pages of journal content have been made available online, a collection dating back to 1799. Wiley-Blackwell publishes on behalf of about 700 professional and scholarly societies. Other major journals published include Angewandte Chemie, Advanced Materials, International Finance and Liver Transplantation. Launched commercially in 1999, Wiley InterScience provided online access to Wiley journals, major reference works, books, including backfile content. Journals from Blackwell Publishing were available online from Blackwell Synergy until they were integrated into Wiley InterScience on June 30, 2008. In December 2007, Wiley began distributing its technical titles through the Safari Books Online e-reference service. On February 17, 2012, Wiley announced the acquisition of Inscape Holdings Inc. which provides DISC assessments and training for interpersonal business skills. Wiley described the acquisition as complementary to the workplace learning products published under its Pfeiffer imprint, one that would help Wiley advance its digital delivery strategy and extend its global reach through Inscape's international distributor network.
On March 7, 2012, Wiley announced its intention to divest assets in the areas of travel, general interest, nautical and crafts, as well as the Webster's New World and CliffsNotes brands. The planned divestiture was aligned with Wiley's "increased strategic focus on content and services for research and professional practices, on lifelong learning through digital technology". On August 13, 2012, Wiley announced it entered into a definitive agreement to sell all of its travel assets, including all of its interests in the Frommer's brand, to Google Inc. On November 6, 2012, Houghton Mifflin Harcourt acquired Wiley's cookbooks and study guides. In 2013, Wiley sold its pets and general interest lines to Turner Publishing Company and its nautical line to Fernhurst Books. H
Logistic regression
In statistics, the logistic model is a used statistical model. In its basic form it uses a logistic function to model a binary dependent variable, although many more complex extensions exist. In regression analysis, logistic regression is estimating the parameters of a logistic model. Mathematically, a binary logistic model has a dependent variable with two possible values, such as pass/fail, win/lose, alive/dead or healthy/sick. In the logistic model, the log-odds for the value labeled "1" is a linear combination of one or more independent variables; the corresponding probability of the value labeled "1" can vary between 1, hence the labeling. The unit of measurement for the log-odds scale is called a logit, from logistic unit, hence the alternative names. Analogous models with a different sigmoid function instead of the logistic function can be used, such as the probit model. Logistic regression was developed by statistician David Cox in 1958; the binary logistic regression model has extensions to more than two levels of the dependent variable: categorical outputs with more than two values are modeled by multinomial logistic regression, if the multiple categories are ordered, by ordinal logistic regression, for example the proportional odds ordinal logistic model.
The model itself models probability of output in terms of input, does not perform statistical classification, though it can be used to make a classifier, for instance by choosing a cutoff value and classifying inputs with probability greater than the cutoff as one class, below the cutoff as the other. The coefficients are not computed by a closed-form expression, unlike linear least squares. Logistic regression is used in various fields, including machine learning, most medical fields, social sciences. For example, the Trauma and Injury Severity Score, used to predict mortality in injured patients, was developed by Boyd et al. using logistic regression. Many other medical scales used to assess severity of a patient have been developed using logistic regression. Logistic regression may be used to predict the risk of developing a given disease, based on observed characteristics of the patient. Another example might be to predict whether an Indian voter will vote BJP or Trinamool Congress or Left Front or Congress, based on age, sex, state of residence, votes in previous elections, etc.
The technique can be used in engineering for predicting the probability of failure of a given process, system or product. It is used in marketing applications such as prediction of a customer's propensity to purchase a product or halt a subscription, etc. In economics it can be used to predict the likelihood of a person's choosing to be in the labor force, a business application would be to predict the likelihood of a homeowner defaulting on a mortgage. Conditional random fields, an extension of logistic regression to sequential data, are used in natural language processing. One may begin to understand logistic regression by first considering a logistic model with given parameters seeing how the coefficients can be estimated from data. Consider a model with two predictors, x 1 and x 2; the general form of the log-odds is: ℓ = β 0 + β 1 x 1 + β 2 x 2, where the coefficients β i are the parameters of the model. Note that this is a linear model: the log-odds ℓ are a linear combination of the predictors x 1 and x 2, including a constant term β 0.
The corresponding odds are the exponent: o = b β 0 + β 1 x 1 + β 2 x 2 where b is the base of the logarithm and exponent. This is now a non-linear model. Odds of o = o: 1 for an event are the same as probability of o / {\displaystyle o/(o
Biochemistry
Biochemistry, sometimes called biological chemistry, is the study of chemical processes within and relating to living organisms. Biochemical processes give rise to the complexity of life. A sub-discipline of both biology and chemistry, biochemistry can be divided in three fields. Over the last decades of the 20th century, biochemistry has through these three disciplines become successful at explaining living processes. All areas of the life sciences are being uncovered and developed by biochemical methodology and research. Biochemistry focuses on understanding how biological molecules give rise to the processes that occur within living cells and between cells, which in turn relates to the study and understanding of tissues and organism structure and function. Biochemistry is related to molecular biology, the study of the molecular mechanisms by which genetic information encoded in DNA is able to result in the processes of life. Much of biochemistry deals with the structures and interactions of biological macromolecules, such as proteins, nucleic acids and lipids, which provide the structure of cells and perform many of the functions associated with life.
The chemistry of the cell depends on the reactions of smaller molecules and ions. These can be inorganic, for example water and metal ions, or organic, for example the amino acids, which are used to synthesize proteins; the mechanisms by which cells harness energy from their environment via chemical reactions are known as metabolism. The findings of biochemistry are applied in medicine and agriculture. In medicine, biochemists investigate the cures of diseases. In nutrition, they study how to maintain health wellness and study the effects of nutritional deficiencies. In agriculture, biochemists investigate soil and fertilizers, try to discover ways to improve crop cultivation, crop storage and pest control. At its broadest definition, biochemistry can be seen as a study of the components and composition of living things and how they come together to become life, in this sense the history of biochemistry may therefore go back as far as the ancient Greeks. However, biochemistry as a specific scientific discipline has its beginning sometime in the 19th century, or a little earlier, depending on which aspect of biochemistry is being focused on.
Some argued that the beginning of biochemistry may have been the discovery of the first enzyme, diastase, in 1833 by Anselme Payen, while others considered Eduard Buchner's first demonstration of a complex biochemical process alcoholic fermentation in cell-free extracts in 1897 to be the birth of biochemistry. Some might point as its beginning to the influential 1842 work by Justus von Liebig, Animal chemistry, or, Organic chemistry in its applications to physiology and pathology, which presented a chemical theory of metabolism, or earlier to the 18th century studies on fermentation and respiration by Antoine Lavoisier. Many other pioneers in the field who helped to uncover the layers of complexity of biochemistry have been proclaimed founders of modern biochemistry, for example Emil Fischer for his work on the chemistry of proteins, F. Gowland Hopkins on enzymes and the dynamic nature of biochemistry; the term "biochemistry" itself is derived from a combination of chemistry. In 1877, Felix Hoppe-Seyler used the term as a synonym for physiological chemistry in the foreword to the first issue of Zeitschrift für Physiologische Chemie where he argued for the setting up of institutes dedicated to this field of study.
The German chemist Carl Neuberg however is cited to have coined the word in 1903, while some credited it to Franz Hofmeister. It was once believed that life and its materials had some essential property or substance distinct from any found in non-living matter, it was thought that only living beings could produce the molecules of life. In 1828, Friedrich Wöhler published a paper on the synthesis of urea, proving that organic compounds can be created artificially. Since biochemistry has advanced since the mid-20th century, with the development of new techniques such as chromatography, X-ray diffraction, dual polarisation interferometry, NMR spectroscopy, radioisotopic labeling, electron microscopy, molecular dynamics simulations; these techniques allowed for the discovery and detailed analysis of many molecules and metabolic pathways of the cell, such as glycolysis and the Krebs cycle, led to an understanding of biochemistry on a molecular level. Philip Randle is well known for his discovery in diabetes research is the glucose-fatty acid cycle in 1963.
He confirmed. High fat oxidation was responsible for the insulin resistance. Another significant historic event in biochemistry is the discovery of the gene, its role in the transfer of information in the cell; this part of biochemistry is called molecular biology. In the 1950s, James D. Watson, Francis Crick, Rosalind Franklin, Maurice Wilkins were instrumental in solving DNA structure and suggesting its relationship with genetic transfer of information. In 1958, George Beadle and Edward Tatum received the Nobel Prize for work in fungi showing that one gene produces one enzyme. In 1988, Colin Pitchfork was the first person convicted of murder with DNA evidence, which led to the growth of forensic science. More Andrew Z. Fire and Craig C. Mello received the 2006 Nobel Prize for discovering the role of RNA interference, in the silencing of gene expression. Around two dozen of the 92
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