Datasets:
qchapp
/
MNLP_M3_rag_documents

Dataset card Data Studio Files
xet
Community
1
id
stringlengths
14
20
title
stringlengths
4
181
text
stringlengths
1
43k
source
stringclasses
1 value
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 nibbles: 10001 + 0110 = 00010111 => 0001 0111 17 + 6 = 23 1 7
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 operations. The Intel 8080, the Zilog Z80 and the CPUs of the x86 family provide the opcode DAA (Decimal Adjust Accumulator).
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 subtraction, consider the following problem: 357 − 432.
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 1000 1011 1111 9 8 11 15 + 0000 0000 0110 0110 0 0 6 6 = 1001 1001 0010 0101 9 9 2 5
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 = 75, so the calculated answer is −75.
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 be calculated. Comparison with pure binary
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 calculating such values. This is useful in financial calculations. Scaling by a power of 10 is simple. Rounding at a decimal digit boundary is simpler. Addition and subtraction in decimal do not require rounding. The alignment of two decimal numbers (for example 1.3 + 27.08) is a simple, exact shift. Conversion to a character form or for display (e.g., to a text-based format such as XML, or to drive signals for a seven-segment display) is a simple per-digit mapping, and can be done in linear (O(n)) time. Conversion from pure binary involves relatively complex logic that spans digits, and for large numbers, no linear-time conversion algorithm is known (see ).
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 binary multiplication, requiring binary shifts and adds or the equivalent, per-digit or group of digits is required). Standard BCD requires four bits per digit, roughly 20 per cent more space than a binary encoding (the ratio of 4 bits to log210 bits is 1.204). When packed so that three digits are encoded in ten bits, the storage overhead is greatly reduced, at the expense of an encoding that is unaligned with the 8-bit byte boundaries common on existing hardware, resulting in slower implementations on these systems. Practical existing implementations of BCD are typically slower than operations on binary representations, especially on embedded systems, due to limited processor support for native BCD operations.
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 of the sign digit may be used to indicate special numeric values, such as infinity, underflow/overflow, and error (a blinking display).
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 (unused) bit combinations are used to add specific telephony characters, with digits similar to those found in telephone keypads original design.
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 as 2.
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 2 or 4 digits after the decimal point are usually enough. Indeed, this is almost a form of fixed point arithmetic since the position of the radix point is implied.
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 digit, for one of the two alternative decimal encodings specified in the IEEE 754-2008 floating-point standard.
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-point algorithms. The MOS 6502 processor has a BCD mode that affects the addition and subtraction instructions. The Psion Organiser 1 handheld computer's manufacturer-supplied software also entirely used BCD to implement floating point; later Psion models used binary exclusively.
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 problem.
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 on the algorithm itself". This was a landmark judgement that determining the patentability of software and algorithms.
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 batches of the Krieger reprint edition were misprints with defective pages 115–146.) (Also: ACM SIGPLAN Notices, Vol. 22 #10, IEEE Computer Society Press #87CH2440-6, October 1987)
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 Genetics
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 Mendel started the genetics studies investigating genetics segregation patterns in families of peas and used statistics to explain the collected data. In the early 1900s, after the rediscovery of Mendel's Mendelian inheritance work, there were gaps in understanding between genetics and evolutionary Darwinism. Francis Galton tried to expand Mendel's discoveries with human data and proposed a different model with fractions of the heredity coming from each ancestral composing an infinite series. He called this the theory of "Law of Ancestral Heredity". His ideas were strongly disagreed by William Bateson, who followed Mendel's conclusions, that genetic inheritance were exclusively from the parents, half from each of them. This led to a vigorous debate between the biometricians, who supported Galton's ideas, as Walter Weldon, Arthur Dukinfield Darbishire and Karl Pearson, and Mendelians, who supported Bateson's (and Mendel's) ideas, such as Charles Davenport and Wilhelm Johannsen. Later, biometricians could not reproduce Galton conclusions in different experiments, and Mendel's ideas prevailed. By the 1930s, models built on statistical reasoning had helped to resolve these differences and to produce the neo-Darwinian modern evolutionary synthesis.
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 of them include the ANOVA, p-value concepts, Fisher's exact test and Fisher's equation for population dynamics. He is credited for the sentence “Natural selection is a mechanism for generating an exceedingly high degree of improbability”. Sewall G. Wright developed F-statistics and methods of computing them and defined inbreeding coefficient. J. B. S. Haldane's book, The Causes of Evolution, reestablished natural selection as the premier mechanism of evolution by explaining it in terms of the mathematical consequences of Mendelian genetics. Also developed the theory of primordial soup.
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 Growth and Form also helped to add quantitative discipline to biological study.
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, saying "Well, I am like a guy who is prospecting for gold along the banks of the Sacramento River in 1849. With a little intelligence, I can reach down and pick up big nuggets of gold. And as long as I can do that, I'm not going to let any people in my department waste scarce resources in placer mining."
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. The research plan might include the research question, the hypothesis to be tested, the experimental design, data collection methods, data analysis perspectives and costs evolved. It is essential to carry the study based on the three basic principles of experimental statistics: randomization, replication, and local control. Research question
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 literature review might be necessary. So, the research can be useful to add value to the scientific community. Hypothesis definition
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 literature review. We can say it is the standard expected answer for the data under the situation in test. In general, HO assumes no association between treatments. On the other hand, the alternative hypothesis is the denial of HO. It assumes some degree of association between the treatment and the outcome. Although, the hypothesis is sustained by question research and its expected and unexpected answers.
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 diets have different effects over animals metabolism (H1: μ1 ≠ μ2).
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 population is not only the individuals, but the total of one specific component of their organisms, as the whole genome, or all the sperm cells, for animals, or the total leaf area, for a plant, for example.
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 catch the most variability across a population. The sample size is determined by several things, since the scope of the research to the resources available. In clinical research, the trial type, as inferiority, equivalence, and superiority is a key in determining sample size.
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 arranged in many ways inside the experiment. In agriculture, the correct experimental design is the root of a good study and the arrangement of treatments within the study is essential because environment largely affects the plots (plants, livestock, microorganisms). These main arrangements can be found in the literature under the names of “lattices”, “incomplete blocks”, “split plot”, “augmented blocks”, and many others. All of the designs might include control plots, determined by the researcher, to provide an error estimation during inference.
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. Data collection Data collection methods must be considered in research planning, because it highly influences the sample size and experimental design.
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 information using instruments.
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 be considered, as high-throughput platforms for phenotyping and genotyping. These tools allow bigger experiments, while turn possible evaluate many plots in lower time than a human-based only method for data collection. Finally, all data collected of interest must be stored in an organized data frame for further analysis. Analysis and data interpretation Descriptive Tools
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, which consists of data arranged in rows and columns, where the frequency is the number of occurrences or repetitions of data. Frequency can be: Absolute: represents the number of times that a determined value appear; Relative: obtained by the division of the absolute frequency by the total number;
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 chart is a graph that shows categorical data as bars presenting heights (vertical bar) or widths (horizontal bar) proportional to represent values. Bar charts provide an image that could also be represented in a tabular format.
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 into uniform or non-uniform classes. It was first introduced by Karl Pearson. Scatter Plot
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 graph, scatter chart, scattergram, or scatter diagram. Mean The arithmetic mean is the sum of a collection of values () divided by the number of items of this collection (). Median The median is the value in the middle of a dataset. Mode
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. Correlation Coefficients Although correlations between two different kinds of data could be inferred by graphs, such as scatter plot, it is necessary validate this though numerical information. For this reason, correlation coefficients are required. They provide a numerical value that reflects the strength of an association.
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 a perfect negative correlation, and ρ = 0 is no linear correlation. Inferential Statistics
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 is possible to test previously defined hypotheses and apply the conclusions to the entire population. The standard error of the mean is a measure of variability that is crucial to do inferences. Hypothesis testing
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 significance, or in other words, the acceptable error rate (α). It is easier to think that we define a critical value that determines the statistical significance when a test statistic is compared with it. So, α also has to be predefined before the experiment. Experiment and statistical analysis: This is when the experiment is really implemented following the appropriate experimental design, data is collected and the more suitable statistical tests are evaluated. Inference: Is made when the null hypothesis is rejected or not rejected, based on the evidence that the comparison of p-values and α brings. It is pointed that the failure to reject H0 just means that there is not enough evidence to support its rejection, but not that this hypothesis is true.
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 multiplication between the standard error of the mean and the confidence level. The calculation of lower value is similar, but instead of a sum, a subtraction must be applied. Statistical considerations Power and statistical error
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 α is the type I error rate and should be chosen before performing the test. The type II error rate is denoted by β and statistical power of the test is 1 − β. p-value
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 significant results. If p is less than α, the null hypothesis (H0) is rejected. Multiple testing
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 global significance level, denoted by α* and each test is individually compared with a value of α = α*/m. This ensures that the familywise error rate in all m tests, is less than or equal to α*. When m is large, the Bonferroni correction may be overly conservative. An alternative to the Bonferroni correction is to control the false discovery rate (FDR). The FDR controls the expected proportion of the rejected null hypotheses (the so-called discoveries) that are false (incorrect rejections). This procedure ensures that, for independent tests, the false discovery rate is at most q*. Thus, the FDR is less conservative than the Bonferroni correction and have more power, at the cost of more false positives.
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 null may be frequently rejected even if the main hypothesis is true. Such rejections are said to be due to model mis-specification. Verifying whether the outcome of a statistical test does not change when the technical assumptions are slightly altered (so-called robustness checks) is the main way of combating mis-specification.
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 biostatistics. Two important changes have been the ability to collect data on a high-throughput scale, and the ability to perform much more complex analysis using computational techniques. This comes from the development in areas as sequencing technologies, Bioinformatics and Machine learning (Machine learning in bioinformatics).
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 signal from the noise. For example, a microarray could be used to measure many thousands of genes simultaneously, determining which of them have different expression in diseased cells compared to normal cells. However, only a fraction of genes will be differentially expressed.
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 the response. In such a case, one could apply the biostatistical technique of dimension reduction (for example via principal component analysis). Classical statistical techniques like linear or logistic regression and linear discriminant analysis do not work well for high dimensional data (i.e. when the number of observations n is smaller than the number of features or predictors p: n < p). As a matter of fact, one can get quite high R2-values despite very low predictive power of the statistical model. These classical statistical techniques (esp. least squares linear regression) were developed for low dimensional data (i.e. where the number of observations n is much larger than the number of predictors p: n >> p). In cases of high dimensionality, one should always consider an independent validation test set and the corresponding residual sum of squares (RSS) and R2 of the validation test set, not those of the training set.
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 advantage of this approach is that it is more robust: It is more likely that a single gene is found to be falsely perturbed than it is that a whole pathway is falsely perturbed. Furthermore, one can integrate the accumulated knowledge about biochemical pathways (like the JAK-STAT signaling pathway) using this approach.
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 articles, as PubMed. Another possibility is search for the desired term (a gene, a protein, a disease, an organism, and so on) and check all results related to this search. There are databases dedicated to SNPs (dbSNP), the knowledge on genes characterization and their pathways (KEGG) and the description of gene function classifying it by cellular component, molecular function and biological process (Gene Ontology). In addition to databases that contain specific molecular information, there are others that are ample in the sense that they store information about an organism or group of organisms. As an example of a database directed towards just one organism, but that contains much data about it, is the Arabidopsis thaliana genetic and molecular database – TAIR. Phytozome, in turn, stores the assemblies and annotation files of dozen of plant genomes, also containing visualization and analysis tools. Moreover, there is an interconnection between some databases in the information exchange/sharing and a major initiative was the International Nucleotide Sequence Database Collaboration (INSDC) which relates data from DDBJ, EMBL-EBI, and NCBI.
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, by using methods of supervised and unsupervised learning, regression, detection of clusters and association rule mining, among others. To indicate some of them, self-organizing maps and k-means are examples of cluster algorithms; neural networks implementation and support vector machines models are examples of common machine learning algorithms.
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 On the other hand, the advent of modern computer technology and relatively cheap computing resources have enabled computer-intensive biostatistical methods like bootstrapping and re-sampling methods.
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 Forests have thus been used for clinical decision support systems. Applications
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 patient with a prognosis of an outcome of a disease.
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 data generated by additional new-omics technologies. Quantitative genetics
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 trait is called Quantitative trait locus (QTL). The study of QTLs become feasible by using molecular markers and measuring traits in populations, but their mapping needs the obtaining of a population from an experimental crossing, like an F2 or Recombinant inbred strains/lines (RILs). To scan for QTLs regions in a genome, a gene map based on linkage have to be built. Some of the best-known QTL mapping algorithms are Interval Mapping, Composite Interval Mapping, and Multiple Interval Mapping.
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 individuals representing a natural population. For this reason, the Genome-wide association study was proposed in order to identify QTLs based on linkage disequilibrium, that is the non-random association between traits and molecular markers. It was leveraged by the development of high-throughput SNP genotyping.
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 environment. So, the concept of Genomic Selection (GS) arises in order to use all molecular markers in the selection and allow the prediction of the performance of candidates in this selection. The proposal is to genotype and phenotype a training population, develop a model that can obtain the genomic estimated breeding values (GEBVs) of individuals belonging to a genotyped and but not phenotyped population, called testing population. This kind of study could also include a validation population, thinking in the concept of cross-validation, in which the real phenotype results measured in this population are compared with the phenotype results based on the prediction, what used to check the accuracy of the model.
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 human genetics Expression data
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/treatment, randomization and blocking, when necessary. In RNA-Seq, the quantification of expression uses the information of mapped reads that are summarized in some genetic unit, as exons that are part of a gene sequence. As microarray results can be approximated by a normal distribution, RNA-Seq counts data are better explained by other distributions. The first used distribution was the Poisson one, but it underestimate the sample error, leading to false positives. Currently, biological variation is considered by methods that estimate a dispersion parameter of a negative binomial distribution. Generalized linear models are used to perform the tests for statistical significance and as the number of genes is high, multiple tests correction have to be considered. Some examples of other analysis on genomics data comes from microarray or proteomics experiments. Often concerning diseases or disease stages.
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 biological data. Most of them are useful in other areas of knowledge, covering a large number of applications (alphabetical). Here are brief descriptions of some of them:
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 possibility to investigate different variance-covariance matrix structures. CycDesigN: A computer package developed by VSNi that helps the researchers create experimental designs and analyze data coming from a design present in one of three classes handled by CycDesigN. These classes are resolvable, non-resolvable, partially replicated and crossover designs. It includes less used designs the Latinized ones, as t-Latinized design. Orange: A programming interface for high-level data processing, data mining and data visualization. Include tools for gene expression and genomics. R: An open source environment and programming language dedicated to statistical computing and graphics. It is an implementation of S language maintained by CRAN. In addition to its functions to read data tables, take descriptive statistics, develop and evaluate models, its repository contains packages developed by researchers around the world. This allows the development of functions written to deal with the statistical analysis of data that comes from specific applications. In the case of Bioinformatics, for example, there are packages located in the main repository (CRAN) and in others, as Bioconductor. It is also possible to use packages under development that are shared in hosting-services as GitHub. SAS: A data analysis software widely used, going through universities, services and industry. Developed by a company with the same name (SAS Institute), it uses SAS language for programming. PLA 3.0: Is a biostatistical analysis software for regulated environments (e.g. drug testing) which supports Quantitative Response Assays (Parallel-Line, Parallel-Logistics, Slope-Ratio) and Dichotomous Assays (Quantal Response, Binary Assays). It also supports weighting methods for combination calculations and the automatic data aggregation of independent assay data. Weka: A Java software for machine learning and data mining, including tools and methods for visualization, clustering, regression, association rule, and classification. There are tools for cross-validation, bootstrapping and a module of algorithm comparison. Weka also can be run in other programming languages as Perl or R.
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 instance, relatively new biostatistics departments have been founded with a focus on bioinformatics and computational biology, whereas older departments, typically affiliated with schools of public health, will have more traditional lines of research involving epidemiological studies and clinical trials as well as bioinformatics. In larger universities around the world, where both a statistics and a biostatistics department exist, the degree of integration between the two departments may range from the bare minimum to very close collaboration. In general, the difference between a statistics program and a biostatistics program is twofold: (i) statistics departments will often host theoretical/methodological research which are less common in biostatistics programs and (ii) statistics departments have lines of research that may include biomedical applications but also other areas such as industry (quality control), business and economics and biological areas other than medicine.
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 Methods in Medical Research Pharmaceutical Statistics Statistics in Medicine See also Bioinformatics Epidemiological method Epidemiology Group size measures Health indicator Mathematical and theoretical biology References External links The International Biometric Society The Collection of Biostatistics Research Archive Guide to Biostatistics (MedPageToday.com) Biomedical Statistics Bioinformatics
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 represented as a subset of the Cartesian product , where belongs to the subset if and only if . Conversely, a subset defines a binary function if and only if for any and , there exists a unique such that belongs to . is then defined to be this .
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 can be thought of as a function. If is the set of integers, is the set of natural numbers (except for zero), and is the set of rational numbers, then division is a binary function .
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 functions of two variables even if their domain does not form a rectangle and thus the cartesian product of two sets.
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 a function from to and a function from to , where is the set of all functions from to , is called currying.
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, because the functions f x and f y are always injective. However, it's not injective in both variables simultaneously, because (for example) f (2,4) = f (1,2).
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 second input is zero. A binary operation is a binary function where the sets X, Y, and Z are all equal; binary operations are often used to define algebraic structures.
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't be linear. However, the bilinear transformation can also be interpreted as a single linear transformation from the tensor product to Z. Generalisations to ternary and other functions
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 of A.
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 morphisms of one variable will work in a closed monoidal category. The category of sets is closed monoidal, but so is the category of vector spaces, giving the notion of bilinear transformation above. References
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 become successful at explaining living processes through these three disciplines. Almost all areas of the life sciences are being uncovered and developed through biochemical methodology and research. Biochemistry focuses on understanding the chemical basis which allows biological molecules to give rise to the processes that occur within living cells and between cells, in turn relating greatly to the understanding of tissues and organs, as well as organism structure and function. Biochemistry is closely related to molecular biology, which is the study of the molecular mechanisms of biological phenomena.
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 reactions of small 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 used by cells to harness energy from their environment via chemical reactions are known as metabolism. The findings of biochemistry are applied primarily in medicine, nutrition and agriculture. In medicine, biochemists investigate the causes and cures of diseases. Nutrition studies how to maintain health and wellness and also the effects of nutritional deficiencies. In agriculture, biochemists investigate soil and fertilizers. Improving crop cultivation, crop storage, and pest control are also goals.
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 began 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 (now called amylase), 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 also 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 even 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. Emil Fischer, who studied the chemistry of proteins, and F. Gowland Hopkins, who studied enzymes and the dynamic nature of biochemistry, represent two examples of early biochemists.
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 argued for the setting up of institutes dedicated to this field of study. The German chemist Carl Neuberg however is often cited to have coined the word in 1903, while some credited it to Franz Hofmeister.
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 his serendipitous urea synthesis from potassium cyanate and ammonium sulfate; some regarded that as a direct overthrow of vitalism and the establishment of organic chemistry. However, the Wöhler synthesis has sparked controversy as some reject the death of vitalism at his hands. Since then, biochemistry has advanced, especially 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 and 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 (citric acid cycle), and led to an understanding of biochemistry on a molecular level.
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 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 recently, Andrew Z. Fire and Craig C. Mello received the 2006 Nobel Prize for discovering the role of RNA interference (RNAi), in the silencing of gene expression.
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 needs, but there are a few differences between plants and animals. For example, ocean algae use bromine, but land plants and animals do not seem to need any. All animals require sodium, but some plants do not. Plants need boron and silicon, but animals may not (or may need ultra-small amounts).
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 amounts of possibly 18 more. Biomolecules
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 monomers are linked together to synthesize a biological polymer, they undergo a process called dehydration synthesis. Different macromolecules can assemble in larger complexes, often needed for biological activity. Carbohydrates
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, as well as play important roles in cell to cell interactions and communications.
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 associated with the sweet taste of fruits, and deoxyribose (C5H10O4), a component of DNA. A monosaccharide can switch between acyclic (open-chain) form and a cyclic form. The open-chain form can be turned into a ring of carbon atoms bridged by an oxygen atom created from the carbonyl group of one end and the hydroxyl group of another. The cyclic molecule has a hemiacetal or hemiketal group, depending on whether the linear form was an aldose or a ketose.
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 glucose may form a hemiacetal linkage between the hydroxyl on carbon 1 and the oxygen on carbon 4, yielding a molecule with a 5-membered ring, called glucofuranose. The same reaction can take place between carbons 1 and 5 to form a molecule with a 6-membered ring, called glucopyranose. Cyclic forms with a 7-atom ring called heptoses are rare.
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 disaccharide is sucrose or ordinary sugar, which consists of a glucose molecule and a fructose molecule joined together. Another important disaccharide is lactose found in milk, consisting of a glucose molecule and a galactose molecule. Lactose may be hydrolysed by lactase, and deficiency in this enzyme results in lactose intolerance.
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, or they may be branched. Two of the most common polysaccharides are cellulose and glycogen, both consisting of repeating glucose monomers. Cellulose is an important structural component of plant's cell walls and glycogen is used as a form of energy storage in animals.
wikipedia