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wiki_50_chunk_38 | Binary-coded decimal | 10001 is the binary, not decimal, representation of the desired result, but the most significant 1 (the "carry") cannot fit in a 4-bit binary number. In BCD as in decimal, there cannot exist a value greater than 9 (1001) per digit. To correct this, 6 (0110) is added to the total, and then the result is treated as two n... | wikipedia |
wiki_50_chunk_39 | Binary-coded decimal | The two nibbles of the result, 0001 and 0111, correspond to the digits "1" and "7". This yields "17" in BCD, which is the correct result. | wikipedia |
wiki_50_chunk_40 | Binary-coded decimal | This technique can be extended to adding multiple digits by adding in groups from right to left, propagating the second digit as a carry, always comparing the 5-bit result of each digit-pair sum to 9. Some CPUs provide a half-carry flag to facilitate BCD arithmetic adjustments following binary addition and subtraction ... | wikipedia |
wiki_50_chunk_41 | Binary-coded decimal | Subtraction
Subtraction is done by adding the ten's complement of the subtrahend to the minuend. To represent the sign of a number in BCD, the number 0000 is used to represent a positive number, and 1001 is used to represent a negative number. The remaining 14 combinations are invalid signs. To illustrate signed BCD s... | wikipedia |
wiki_50_chunk_42 | Binary-coded decimal | In signed BCD, 357 is 0000 0011 0101 0111. The ten's complement of 432 can be obtained by taking the nine's complement of 432, and then adding one. So, 999 − 432 = 567, and 567 + 1 = 568. By preceding 568 in BCD by the negative sign code, the number −432 can be represented. So, −432 in signed BCD is 1001 0101 0110 1000... | wikipedia |
wiki_50_chunk_43 | Binary-coded decimal | Now that both numbers are represented in signed BCD, they can be added together:
0000 0011 0101 0111
0 3 5 7
+ 1001 0101 0110 1000
9 5 6 8
= 1001 1000 1011 1111
9 8 11 15 | wikipedia |
wiki_50_chunk_44 | Binary-coded decimal | Since BCD is a form of decimal representation, several of the digit sums above are invalid. In the event that an invalid entry (any BCD digit greater than 1001) exists, 6 is added to generate a carry bit and cause the sum to become a valid entry. So, adding 6 to the invalid entries results in the following:
1001 100... | wikipedia |
wiki_50_chunk_45 | Binary-coded decimal | Thus the result of the subtraction is 1001 1001 0010 0101 (−925). To confirm the result, note that the first digit is 9, which means negative. This seems to be correct since 357 − 432 should result in a negative number. The remaining nibbles are BCD, so 1001 0010 0101 is 925. The ten's complement of 925 is 1000 − 925 =... | wikipedia |
wiki_50_chunk_46 | Binary-coded decimal | If there are a different number of nibbles being added together (such as 1053 − 2), the number with the fewer digits must first be prefixed with zeros before taking the ten's complement or subtracting. So, with 1053 − 2, 2 would have to first be represented as 0002 in BCD, and the ten's complement of 0002 would have to... | wikipedia |
wiki_50_chunk_47 | Binary-coded decimal | Advantages
Many non-integral values, such as decimal 0.2, have an infinite place-value representation in binary (.001100110011...) but have a finite place-value in binary-coded decimal (0.0010). Consequently, a system based on binary-coded decimal representations of decimal fractions avoids errors representing and cal... | wikipedia |
wiki_50_chunk_48 | Binary-coded decimal | Disadvantages
Some operations are more complex to implement. Adders require extra logic to cause them to wrap and generate a carry early. 15 to 20 per cent more circuitry is needed for BCD add compared to pure binary. Multiplication requires the use of algorithms that are somewhat more complex than shift-mask-add (a b... | wikipedia |
wiki_50_chunk_49 | Binary-coded decimal | Representational variations
Various BCD implementations exist that employ other representations for numbers. Programmable calculators manufactured by Texas Instruments, Hewlett-Packard, and others typically employ a floating-point BCD format, typically with two or three digits for the (decimal) exponent. The extra bits... | wikipedia |
wiki_50_chunk_50 | Binary-coded decimal | Signed variations
Signed decimal values may be represented in several ways. The COBOL programming language, for example, supports five zoned decimal formats, with each one encoding the numeric sign in a different way: Telephony binary-coded decimal (TBCD)
3GPP developed TBCD, an expansion to BCD where the remaining (un... | wikipedia |
wiki_50_chunk_51 | Binary-coded decimal | The mentioned 3GPP document defines TBCD-STRING with swapped nibbles in each byte. Bits, octets and digits indexed from 1, bits from the right, digits and octets from the left.
bits 8765 of octet n encoding digit 2n bits 4321 of octet n encoding digit 2(n – 1) + 1 Meaning number 1234, would become 21 43 in TBCD. | wikipedia |
wiki_50_chunk_52 | Binary-coded decimal | Alternative encodings
If errors in representation and computation are more important than the speed of conversion to and from display, a scaled binary representation may be used, which stores a decimal number as a binary-encoded integer and a binary-encoded signed decimal exponent. For example, 0.2 can be represented a... | wikipedia |
wiki_50_chunk_53 | Binary-coded decimal | This representation allows rapid multiplication and division, but may require shifting by a power of 10 during addition and subtraction to align the decimal points. It is appropriate for applications with a fixed number of decimal places that do not then require this adjustment—particularly financial applications where... | wikipedia |
wiki_50_chunk_54 | Binary-coded decimal | The Hertz and Chen–Ho encodings provide Boolean transformations for converting groups of three BCD-encoded digits to and from 10-bit values that can be efficiently encoded in hardware with only 2 or 3 gate delays. Densely packed decimal (DPD) is a similar scheme that is used for most of the significand, except the lead... | wikipedia |
wiki_50_chunk_55 | Binary-coded decimal | Application
The BIOS in many personal computers stores the date and time in BCD because the MC6818 real-time clock chip used in the original IBM PC AT motherboard provided the time encoded in BCD. This form is easily converted into ASCII for display. The Atari 8-bit family of computers used BCD to implement floating-po... | wikipedia |
wiki_50_chunk_56 | Binary-coded decimal | Early models of the PlayStation 3 store the date and time in BCD. This led to a worldwide outage of the console on 1 March 2010. The last two digits of the year stored as BCD were misinterpreted as 16 causing an error in the unit's date, rendering most functions inoperable. This has been referred to as the Year 2010 pr... | wikipedia |
wiki_50_chunk_57 | Binary-coded decimal | Legal history
In the 1972 case Gottschalk v. Benson, the U.S. Supreme Court overturned a lower court's decision that had allowed a patent for converting BCD-encoded numbers to binary on a computer. The decision noted that a patent "would wholly pre-empt the mathematical formula and in practical effect would be a patent... | wikipedia |
wiki_50_chunk_58 | Binary-coded decimal | See also
Bi-quinary coded decimal
Binary-coded ternary (BCT)
Binary integer decimal (BID)
Bitmask
Chen–Ho encoding
Decimal computer
Densely packed decimal (DPD)
Double dabble, an algorithm for converting binary numbers to BCD
Year 2000 problem Notes References Further reading
and (NB. At least some bat... | wikipedia |
wiki_50_chunk_59 | Binary-coded decimal | External links
Convert BCD to decimal, binary and hexadecimal and vice versa
BCD for Java Computer arithmetic
Numeral systems
Non-standard positional numeral systems
Binary arithmetic
Articles with example C code | wikipedia |
wiki_51_chunk_0 | Biostatistics | Biostatistics (also known as biometry) are the development and application of statistical methods to a wide range of topics in biology. It encompasses the design of biological experiments, the collection and analysis of data from those experiments and the interpretation of the results. History Biostatistics and Genetic... | wikipedia |
wiki_51_chunk_1 | Biostatistics | Biostatistical modeling forms an important part of numerous modern biological theories. Genetics studies, since its beginning, used statistical concepts to understand observed experimental results. Some genetics scientists even contributed with statistical advances with the development of methods and tools. Gregor Mend... | wikipedia |
wiki_51_chunk_2 | Biostatistics | Solving these differences also allowed to define the concept of population genetics and brought together genetics and evolution. The three leading figures in the establishment of population genetics and this synthesis all relied on statistics and developed its use in biology. | wikipedia |
wiki_51_chunk_3 | Biostatistics | Ronald Fisher developed several basic statistical methods in support of his work studying the crop experiments at Rothamsted Research, including in his books Statistical Methods for Research Workers (1925) end The Genetical Theory of Natural Selection (1930). He gave many contributions to genetics and statistics. Some ... | wikipedia |
wiki_51_chunk_4 | Biostatistics | These and other biostatisticians, mathematical biologists, and statistically inclined geneticists helped bring together evolutionary biology and genetics into a consistent, coherent whole that could begin to be quantitatively modeled. In parallel to this overall development, the pioneering work of D'Arcy Thompson in On... | wikipedia |
wiki_51_chunk_5 | Biostatistics | Despite the fundamental importance and frequent necessity of statistical reasoning, there may nonetheless have been a tendency among biologists to distrust or deprecate results which are not qualitatively apparent. One anecdote describes Thomas Hunt Morgan banning the Friden calculator from his department at Caltech, s... | wikipedia |
wiki_51_chunk_6 | Biostatistics | Research planning Any research in life sciences is proposed to answer a scientific question we might have. To answer this question with a high certainty, we need accurate results. The correct definition of the main hypothesis and the research plan will reduce errors while taking a decision in understanding a phenomenon... | wikipedia |
wiki_51_chunk_7 | Biostatistics | The research question will define the objective of a study. The research will be headed by the question, so it needs to be concise, at the same time it is focused on interesting and novel topics that may improve science and knowledge and that field. To define the way to ask the scientific question, an exhaustive litera... | wikipedia |
wiki_51_chunk_8 | Biostatistics | Once the aim of the study is defined, the possible answers to the research question can be proposed, transforming this question into a hypothesis. The main propose is called null hypothesis (H0) and is usually based on a permanent knowledge about the topic or an obvious occurrence of the phenomena, sustained by a deep ... | wikipedia |
wiki_51_chunk_9 | Biostatistics | As an example, consider groups of similar animals (mice, for example) under two different diet systems. The research question would be: what is the best diet? In this case, H0 would be that there is no difference between the two diets in mice metabolism (H0: μ1 = μ2) and the alternative hypothesis would be that the die... | wikipedia |
wiki_51_chunk_10 | Biostatistics | The hypothesis is defined by the researcher, according to his/her interests in answering the main question. Besides that, the alternative hypothesis can be more than one hypothesis. It can assume not only differences across observed parameters, but their degree of differences (i.e. higher or shorter). Sampling | wikipedia |
wiki_51_chunk_11 | Biostatistics | Usually, a study aims to understand an effect of a phenomenon over a population. In biology, a population is defined as all the individuals of a given species, in a specific area at a given time. In biostatistics, this concept is extended to a variety of collections possible of study. Although, in biostatistics, a popu... | wikipedia |
wiki_51_chunk_12 | Biostatistics | It is not possible to take the measures from all the elements of a population. Because of that, the sampling process is very important for statistical inference. Sampling is defined as to randomly get a representative part of the entire population, to make posterior inferences about the population. So, the sample might... | wikipedia |
wiki_51_chunk_13 | Biostatistics | Experimental design
Experimental designs sustain those basic principles of experimental statistics. There are three basic experimental designs to randomly allocate treatments in all plots of the experiment. They are completely randomized design, randomized block design, and factorial designs. Treatments can be arrange... | wikipedia |
wiki_51_chunk_14 | Biostatistics | In clinical studies, the samples are usually smaller than in other biological studies, and in most cases, the environment effect can be controlled or measured. It is common to use randomized controlled clinical trials, where results are usually compared with observational study designs such as case–control or cohort. D... | wikipedia |
wiki_51_chunk_15 | Biostatistics | Data collection varies according to type of data. For qualitative data, collection can be done with structured questionnaires or by observation, considering presence or intensity of disease, using score criterion to categorize levels of occurrence. For quantitative data, collection is done by measuring numerical inform... | wikipedia |
wiki_51_chunk_16 | Biostatistics | In agriculture and biology studies, yield data and its components can be obtained by metric measures. However, pest and disease injuries in plats are obtained by observation, considering score scales for levels of damage. Especially, in genetic studies, modern methods for data collection in field and laboratory should ... | wikipedia |
wiki_51_chunk_17 | Biostatistics | Data can be represented through tables or graphical representation, such as line charts, bar charts, histograms, scatter plot. Also, measures of central tendency and variability can be very useful to describe an overview of the data. Follow some examples: Frequency tables One type of tables are the frequency table, whi... | wikipedia |
wiki_51_chunk_18 | Biostatistics | In the next example, we have the number of genes in ten operons of the same organism. Line graph Line graphs represent the variation of a value over another metric, such as time. In general, values are represented in the vertical axis, while the time variation is represented in the horizontal axis. Bar chart A bar char... | wikipedia |
wiki_51_chunk_19 | Biostatistics | In the bar chart example, we have the birth rate in Brazil for the December months from 2010 to 2016. The sharp fall in December 2016 reflects the outbreak of Zika virus in the birth rate in Brazil. Histograms The histogram (or frequency distribution) is a graphical representation of a dataset tabulated and divided int... | wikipedia |
wiki_51_chunk_20 | Biostatistics | A scatter plot is a mathematical diagram that uses Cartesian coordinates to display values of a dataset. A scatter plot shows the data as a set of points, each one presenting the value of one variable determining the position on the horizontal axis and another variable on the vertical axis. They are also called scatter... | wikipedia |
wiki_51_chunk_21 | Biostatistics | The mode is the value of a set of data that appears most often. Box Plot
Box plot is a method for graphically depicting groups of numerical data. The maximum and minimum values are represented by the lines, and the interquartile range (IQR) represent 25–75% of the data. Outliers may be plotted as circles. Correlatio... | wikipedia |
wiki_51_chunk_22 | Biostatistics | Pearson Correlation Coefficient Pearson correlation coefficient is a measure of association between two variables, X and Y. This coefficient, usually represented by ρ (rho) for the population and r for the sample, assumes values between −1 and 1, where ρ = 1 represents a perfect positive correlation, ρ = −1 represents... | wikipedia |
wiki_51_chunk_23 | Biostatistics | It is used to make inferences about an unknown population, by estimation and/or hypothesis testing. In other words, it is desirable to obtain parameters to describe the population of interest, but since the data is limited, it is necessary to make use of a representative sample in order to estimate them. With that, it ... | wikipedia |
wiki_51_chunk_24 | Biostatistics | Hypothesis testing is essential to make inferences about populations aiming to answer research questions, as settled in "Research planning" section. Authors defined four steps to be set: | wikipedia |
wiki_51_chunk_25 | Biostatistics | The hypothesis to be tested: as stated earlier, we have to work with the definition of a null hypothesis (H0), that is going to be tested, and an alternative hypothesis. But they must be defined before the experiment implementation.
Significance level and decision rule: A decision rule depends on the level of signifi... | wikipedia |
wiki_51_chunk_26 | Biostatistics | Confidence intervals A confidence interval is a range of values that can contain the true real parameter value in given a certain level of confidence. The first step is to estimate the best-unbiased estimate of the population parameter. The upper value of the interval is obtained by the sum of this estimate with the mu... | wikipedia |
wiki_51_chunk_27 | Biostatistics | When testing a hypothesis, there are two types of statistic errors possible: Type I error and Type II error. The type I error or false positive is the incorrect rejection of a true null hypothesis and the type II error or false negative is the failure to reject a false null hypothesis. The significance level denoted by... | wikipedia |
wiki_51_chunk_28 | Biostatistics | The p-value is the probability of obtaining results as extreme as or more extreme than those observed, assuming the null hypothesis (H0) is true. It is also called the calculated probability. It is common to confuse the p-value with the significance level (α), but, the α is a predefined threshold for calling significan... | wikipedia |
wiki_51_chunk_29 | Biostatistics | In multiple tests of the same hypothesis, the probability of the occurrence of falses positives (familywise error rate) increase and some strategy are used to control this occurrence. This is commonly achieved by using a more stringent threshold to reject null hypotheses. The Bonferroni correction defines an acceptable... | wikipedia |
wiki_51_chunk_30 | Biostatistics | Mis-specification and robustness checks | wikipedia |
wiki_51_chunk_31 | Biostatistics | The main hypothesis being tested (e.g., no association between treatments and outcomes) is often accompanied by other technical assumptions (e.g., about the form of the probability distribution of the outcomes) that are also part of the null hypothesis. When the technical assumptions are violated in practice, then the ... | wikipedia |
wiki_51_chunk_32 | Biostatistics | Model selection criteria Model criteria selection will select or model that more approximate true model. The Akaike's Information Criterion (AIC) and The Bayesian Information Criterion (BIC) are examples of asymptotically efficient criteria. Developments and Big Data Recent developments have made a large impact on bios... | wikipedia |
wiki_51_chunk_33 | Biostatistics | Use in high-throughput data New biomedical technologies like microarrays, next-generation sequencers (for genomics) and mass spectrometry (for proteomics) generate enormous amounts of data, allowing many tests to be performed simultaneously. Careful analysis with biostatistical methods is required to separate the signa... | wikipedia |
wiki_51_chunk_34 | Biostatistics | Multicollinearity often occurs in high-throughput biostatistical settings. Due to high intercorrelation between the predictors (such as gene expression levels), the information of one predictor might be contained in another one. It could be that only 5% of the predictors are responsible for 90% of the variability of th... | wikipedia |
wiki_51_chunk_35 | Biostatistics | Often, it is useful to pool information from multiple predictors together. For example, Gene Set Enrichment Analysis (GSEA) considers the perturbation of whole (functionally related) gene sets rather than of single genes. These gene sets might be known biochemical pathways or otherwise functionally related genes. The a... | wikipedia |
wiki_51_chunk_36 | Biostatistics | Bioinformatics advances in databases, data mining, and biological interpretation | wikipedia |
wiki_51_chunk_37 | Biostatistics | The development of biological databases enables storage and management of biological data with the possibility of ensuring access for users around the world. They are useful for researchers depositing data, retrieve information and files (raw or processed) originated from other experiments or indexing scientific articl... | wikipedia |
wiki_51_chunk_38 | Biostatistics | Nowadays, increase in size and complexity of molecular datasets leads to use of powerful statistical methods provided by computer science algorithms which are developed by machine learning area. Therefore, data mining and machine learning allow detection of patterns in data with a complex structure, as biological ones,... | wikipedia |
wiki_51_chunk_39 | Biostatistics | Collaborative work among molecular biologists, bioinformaticians, statisticians and computer scientists is important to perform an experiment correctly, going from planning, passing through data generation and analysis, and ending with biological interpretation of the results. Use of computationally intensive methods O... | wikipedia |
wiki_51_chunk_40 | Biostatistics | In recent times, random forests have gained popularity as a method for performing statistical classification. Random forest techniques generate a panel of decision trees. Decision trees have the advantage that you can draw them and interpret them (even with a basic understanding of mathematics and statistics). Random F... | wikipedia |
wiki_51_chunk_41 | Biostatistics | Public health
Public health, including epidemiology, health services research, nutrition, environmental health and health care policy & management. In these medicine contents, it's important to consider the design and analysis of the clinical trials. As one example, there is the assessment of severity state of a patie... | wikipedia |
wiki_51_chunk_42 | Biostatistics | With new technologies and genetics knowledge, biostatistics are now also used for Systems medicine, which consists in a more personalized medicine. For this, is made an integration of data from different sources, including conventional patient data, clinico-pathological parameters, molecular and genetic data as well as... | wikipedia |
wiki_51_chunk_43 | Biostatistics | The study of Population genetics and Statistical genetics in order to link variation in genotype with a variation in phenotype. In other words, it is desirable to discover the genetic basis of a measurable trait, a quantitative trait, that is under polygenic control. A genome region that is responsible for a continuous... | wikipedia |
wiki_51_chunk_44 | Biostatistics | However, QTL mapping resolution is impaired by the amount of recombination assayed, a problem for species in which it is difficult to obtain large offspring. Furthermore, allele diversity is restricted to individuals originated from contrasting parents, which limit studies of allele diversity when we have a panel of in... | wikipedia |
wiki_51_chunk_45 | Biostatistics | In animal and plant breeding, the use of markers in selection aiming for breeding, mainly the molecular ones, collaborated to the development of marker-assisted selection. While QTL mapping is limited due resolution, GWAS does not have enough power when rare variants of small effect that are also influenced by environm... | wikipedia |
wiki_51_chunk_46 | Biostatistics | As a summary, some points about the application of quantitative genetics are:
This has been used in agriculture to improve crops (Plant breeding) and livestock (Animal breeding).
In biomedical research, this work can assist in finding candidates gene alleles that can cause or influence predisposition to diseases in ... | wikipedia |
wiki_51_chunk_47 | Biostatistics | Studies for differential expression of genes from RNA-Seq data, as for RT-qPCR and microarrays, demands comparison of conditions. The goal is to identify genes which have a significant change in abundance between different conditions. Then, experiments are designed appropriately, with replicates for each condition/trea... | wikipedia |
wiki_51_chunk_48 | Biostatistics | Other studies Ecology, ecological forecasting
Biological sequence analysis
Systems biology for gene network inference or pathways analysis.
Population dynamics, especially in regards to fisheries science.
Phylogenetics and evolution Tools There are a lot of tools that can be used to do statistical analysis in biolo... | wikipedia |
wiki_51_chunk_49 | Biostatistics | ASReml: Another software developed by VSNi that can be used also in R environment as a package. It is developed to estimate variance components under a general linear mixed model using restricted maximum likelihood (REML). Models with fixed effects and random effects and nested or crossed ones are allowed. Gives the po... | wikipedia |
wiki_51_chunk_50 | Biostatistics | Scope and training programs Almost all educational programmes in biostatistics are at postgraduate level. They are most often found in schools of public health, affiliated with schools of medicine, forestry, or agriculture, or as a focus of application in departments of statistics. | wikipedia |
wiki_51_chunk_51 | Biostatistics | In the United States, where several universities have dedicated biostatistics departments, many other top-tier universities integrate biostatistics faculty into statistics or other departments, such as epidemiology. Thus, departments carrying the name "biostatistics" may exist under quite different structures. For inst... | wikipedia |
wiki_51_chunk_52 | Biostatistics | Specialized journals Biostatistics
International Journal of Biostatistics
Journal of Epidemiology and Biostatistics
Biostatistics and Public Health
Biometrics
Biometrika
Biometrical Journal
Communications in Biometry and Crop Science
Statistical Applications in Genetics and Molecular Biology
Statistical Method... | wikipedia |
wiki_52_chunk_0 | Binary function | In mathematics, a binary function (also called bivariate function, or function of two variables) is a function that takes two inputs. Precisely stated, a function is binary if there exists sets such that where is the Cartesian product of and Alternative definitions
Set-theoretically, a binary function can be repres... | wikipedia |
wiki_52_chunk_1 | Binary function | Alternatively, a binary function may be interpreted as simply a function from to .
Even when thought of this way, however, one generally writes instead of .
(That is, the same pair of parentheses is used to indicate both function application and the formation of an ordered pair.) Examples
Division of whole numbers ca... | wikipedia |
wiki_52_chunk_2 | Binary function | Another example is that of inner products, or more generally functions of the form , where , are real-valued vectors of appropriate size and is a matrix. If is a positive definite matrix, this yields an inner product. Functions of two real variables
Functions whose domain is a subset of are often also called functi... | wikipedia |
wiki_52_chunk_3 | Binary function | Restrictions to ordinary functions
In turn, one can also derive ordinary functions of one variable from a binary function.
Given any element , there is a function , or , from to , given by .
Similarly, given any element , there is a function , or , from to , given by . In computer science, this identification between... | wikipedia |
wiki_52_chunk_4 | Binary function | Generalisations
The various concepts relating to functions can also be generalised to binary functions.
For example, the division example above is surjective (or onto) because every rational number may be expressed as a quotient of an integer and a natural number.
This example is injective in each input separately, bec... | wikipedia |
wiki_52_chunk_5 | Binary function | One can also consider partial binary functions, which may be defined only for certain values of the inputs.
For example, the division example above may also be interpreted as a partial binary function from Z and N to Q, where N is the set of all natural numbers, including zero.
But this function is undefined when the s... | wikipedia |
wiki_52_chunk_6 | Binary function | In linear algebra, a bilinear transformation is a binary function where the sets X, Y, and Z are all vector spaces and the derived functions f x and fy are all linear transformations.
A bilinear transformation, like any binary function, can be interpreted as a function from X × Y to Z, but this function in general won'... | wikipedia |
wiki_52_chunk_7 | Binary function | The concept of binary function generalises to ternary (or 3-ary) function, quaternary (or 4-ary) function, or more generally to n-ary function for any natural number n.
A 0-ary function to Z is simply given by an element of Z.
One can also define an A-ary function where A is any set; there is one input for each element... | wikipedia |
wiki_52_chunk_8 | Binary function | Category theory
In category theory, n-ary functions generalise to n-ary morphisms in a multicategory.
The interpretation of an n-ary morphism as an ordinary morphisms whose domain is some sort of product of the domains of the original n-ary morphism will work in a monoidal category.
The construction of the derived morp... | wikipedia |
wiki_52_chunk_9 | Binary function | Types of functions
2 (number) | wikipedia |
wiki_53_chunk_0 | Biochemistry | Biochemistry or biological chemistry, is the study of chemical processes within and relating to living organisms. A sub-discipline of both chemistry and biology, biochemistry may be divided into three fields: structural biology, enzymology and metabolism. Over the last decades of the 20th century, biochemistry has be... | wikipedia |
wiki_53_chunk_1 | Biochemistry | Much of biochemistry deals with the structures, bonding, functions, and interactions of biological macromolecules, such as proteins, nucleic acids, carbohydrates, and lipids. They provide the structure of cells and perform many of the functions associated with life. The chemistry of the cell also depends upon the rea... | wikipedia |
wiki_53_chunk_2 | Biochemistry | History | wikipedia |
wiki_53_chunk_3 | Biochemistry | At its most comprehensive 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... | wikipedia |
wiki_53_chunk_4 | Biochemistry | The term "biochemistry" itself is derived from a combination of biology and chemistry. In 1877, Felix Hoppe-Seyler used the term (biochemie in German) as a synonym for physiological chemistry in the foreword to the first issue of Zeitschrift für Physiologische Chemie (Journal of Physiological Chemistry) where he argue... | wikipedia |
wiki_53_chunk_5 | Biochemistry | It was once generally believed that life and its materials had some essential property or substance (often referred to as the "vital principle") distinct from any found in non-living matter, and it was thought that only living beings could produce the molecules of life. In 1828, Friedrich Wöhler published a paper on hi... | wikipedia |
wiki_53_chunk_6 | Biochemistry | Another significant historic event in biochemistry is the discovery of the gene, and its role in the transfer of information in the cell. In the 1950s, James D. Watson, Francis Crick, Rosalind Franklin and Maurice Wilkins were instrumental in solving DNA structure and suggesting its relationship with the genetic transf... | wikipedia |
wiki_53_chunk_7 | Biochemistry | Starting materials: the chemical elements of life Around two dozen chemical elements are essential to various kinds of biological life. Most rare elements on Earth are not needed by life (exceptions being selenium and iodine), while a few common ones (aluminum and titanium) are not used. Most organisms share element n... | wikipedia |
wiki_53_chunk_8 | Biochemistry | Just six elements—carbon, hydrogen, nitrogen, oxygen, calcium and phosphorus—make up almost 99% of the mass of living cells, including those in the human body (see composition of the human body for a complete list). In addition to the six major elements that compose most of the human body, humans require smaller amount... | wikipedia |
wiki_53_chunk_9 | Biochemistry | The 4 main classes of molecules in bio-chemistry (often called biomolecules) are carbohydrates, lipids, proteins, and nucleic acids. Many biological molecules are polymers: in this terminology, monomers are relatively small macromolecules that are linked together to create large macromolecules known as polymers. When m... | wikipedia |
wiki_53_chunk_10 | Biochemistry | Two of the main functions of carbohydrates are energy storage and providing structure. One of the common sugars known as glucose is carbohydrate, but not all carbohydrates are sugars. There are more carbohydrates on Earth than any other known type of biomolecule; they are used to store energy and genetic information, a... | wikipedia |
wiki_53_chunk_11 | Biochemistry | The simplest type of carbohydrate is a monosaccharide, which among other properties contains carbon, hydrogen, and oxygen, mostly in a ratio of 1:2:1 (generalized formula CnH2nOn, where n is at least 3). Glucose (C6H12O6) is one of the most important carbohydrates; others include fructose (C6H12O6), the sugar commonly... | wikipedia |
wiki_53_chunk_12 | Biochemistry | In these cyclic forms, the ring usually has 5 or 6 atoms. These forms are called furanoses and pyranoses, respectively—by analogy with furan and pyran, the simplest compounds with the same carbon-oxygen ring (although they lack the carbon-carbon double bonds of these two molecules). For example, the aldohexose glucos... | wikipedia |
wiki_53_chunk_13 | Biochemistry | Two monosaccharides can be joined together by a glycosidic or ester bond into a disaccharide through a dehydration reaction during which a molecule of water is released. The reverse reaction in which the glycosidic bond of a disaccharide is broken into two monosaccharides is termed hydrolysis. The best-known disacchar... | wikipedia |
wiki_53_chunk_14 | Biochemistry | When a few (around three to six) monosaccharides are joined, it is called an oligosaccharide (oligo- meaning "few"). These molecules tend to be used as markers and signals, as well as having some other uses. Many monosaccharides joined together form a polysaccharide. They can be joined together in one long linear chain... | wikipedia |
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