Wavelet transformIn mathematics, a wavelet series is a representation of a square-integrable (real- or complex-valued) function by a certain orthonormal series generated by a wavelet. This article provides a formal, mathematical definition of an orthonormal wavelet and of the integral wavelet transform. A function is called an orthonormal wavelet if it can be used to define a Hilbert basis, that is a complete orthonormal system, for the Hilbert space of square integrable functions.
WaveletA wavelet is a wave-like oscillation with an amplitude that begins at zero, increases or decreases, and then returns to zero one or more times. Wavelets are termed a "brief oscillation". A taxonomy of wavelets has been established, based on the number and direction of its pulses. Wavelets are imbued with specific properties that make them useful for signal processing. For example, a wavelet could be created to have a frequency of Middle C and a short duration of roughly one tenth of a second.
Discrete wavelet transformIn numerical analysis and functional analysis, a discrete wavelet transform (DWT) is any wavelet transform for which the wavelets are discretely sampled. As with other wavelet transforms, a key advantage it has over Fourier transforms is temporal resolution: it captures both frequency and location information (location in time). Haar wavelet The first DWT was invented by Hungarian mathematician Alfréd Haar. For an input represented by a list of numbers, the Haar wavelet transform may be considered to pair up input values, storing the difference and passing the sum.
DNADeoxyribonucleic acid (diːˈɒksᵻˌraɪboʊnjuːˌkliːᵻk,_-ˌkleɪ-; DNA) is a polymer composed of two polynucleotide chains that coil around each other to form a double helix. The polymer carries genetic instructions for the development, functioning, growth and reproduction of all known organisms and many viruses. DNA and ribonucleic acid (RNA) are nucleic acids. Alongside proteins, lipids and complex carbohydrates (polysaccharides), nucleic acids are one of the four major types of macromolecules that are essential for all known forms of life.
Continuous wavelet transformIn mathematics, the continuous wavelet transform (CWT) is a formal (i.e., non-numerical) tool that provides an overcomplete representation of a signal by letting the translation and scale parameter of the wavelets vary continuously. The continuous wavelet transform of a function at a scale (a>0) and translational value is expressed by the following integral where is a continuous function in both the time domain and the frequency domain called the mother wavelet and the overline represents operation of complex conjugate.
Haar waveletIn mathematics, the Haar wavelet is a sequence of rescaled "square-shaped" functions which together form a wavelet family or basis. Wavelet analysis is similar to Fourier analysis in that it allows a target function over an interval to be represented in terms of an orthonormal basis. The Haar sequence is now recognised as the first known wavelet basis and is extensively used as a teaching example. The Haar sequence was proposed in 1909 by Alfréd Haar.
Chromosome 22Chromosome 22 is one of the 23 pairs of chromosomes in human cells. Humans normally have two copies of chromosome 22 in each cell. Chromosome 22 is the second smallest human chromosome, spanning about 51 million DNA base pairs and representing between 1.5 and 2% of the total DNA in cells. In 1999, researchers working on the Human Genome Project announced they had determined the sequence of base pairs that make up this chromosome. Chromosome 22 was the first human chromosome to be fully sequenced.
Chromosome 21Chromosome 21 is one of the 23 pairs of chromosomes in humans. Chromosome 21 is both the smallest human autosome and chromosome, with 45 million base pairs (the building material of DNA) representing about 1.5 percent of the total DNA in cells. Most people have two copies of chromosome 21, while those with three copies of chromosome 21 have Down syndrome, also called "trisomy 21". Researchers working on the Human Genome Project announced in May 2000 that they had determined the sequence of base pairs that make up this chromosome.
Morlet waveletIn mathematics, the Morlet wavelet (or Gabor wavelet) is a wavelet composed of a complex exponential (carrier) multiplied by a Gaussian window (envelope). This wavelet is closely related to human perception, both hearing and vision. Wavelet#History In 1946, physicist Dennis Gabor, applying ideas from quantum physics, introduced the use of Gaussian-windowed sinusoids for time-frequency decomposition, which he referred to as atoms, and which provide the best trade-off between spatial and frequency resolution.
Chromosome 2Chromosome 2 is one of the twenty-three pairs of chromosomes in humans. People normally have two copies of this chromosome. Chromosome 2 is the second-largest human chromosome, spanning more than 242 million base pairs and representing almost eight percent of the total DNA in human cells. Chromosome 2 contains the HOXD homeobox gene cluster. Humans have only twenty-three pairs of chromosomes, while all other extant members of Hominidae have twenty-four pairs. It is believed that Neanderthals and Denisovans had twenty-three pairs.
X chromosomeThe X chromosome is one of the two sex chromosomes in many organisms, including mammals, and is found in both males and females. It is a part of the XY sex-determination system and XO sex-determination system. The X chromosome was named for its unique properties by early researchers, which resulted in the naming of its counterpart Y chromosome, for the next letter in the alphabet, following its subsequent discovery. It was first noted that the X chromosome was special in 1890 by Hermann Henking in Leipzig.
ChromosomeA chromosome is a long DNA molecule with part or all of the genetic material of an organism. In most chromosomes the very long thin DNA fibers are coated with packaging proteins; in eukaryotic cells the most important of these proteins are the histones. These proteins, aided by chaperone proteins, bind to and condense the DNA molecule to maintain its integrity. These chromosomes display a complex three-dimensional structure, which plays a significant role in transcriptional regulation.
Nucleic acid sequenceA nucleic acid sequence is a succession of bases within the nucleotides forming alleles within a DNA (using GACT) or RNA (GACU) molecule. This succession is denoted by a series of a set of five different letters that indicate the order of the nucleotides. By convention, sequences are usually presented from the 5' end to the 3' end. For DNA, with its double helix, there are two possible directions for the notated sequence; of these two, the sense strand is used.
Chromosome 9fChromosome 9 is one of the 23 pairs of chromosomes in humans. Humans normally have two copies of this chromosome, as they normally do with all chromosomes. Chromosome 9 spans about 150 million base pairs of nucleic acids (the building blocks of DNA) and represents between 4.0 and 4.5% of the total DNA in cells. These are some of the gene count estimates of human chromosome 9. Because researchers use different approaches to genome annotation, their predictions of the number of genes on each chromosome varies (for technical details, see gene prediction).
Y chromosomeThe Y chromosome is one of two sex chromosomes in therian mammals and other organisms. The other sex chromosome is the X chromosome. Y is normally the sex-determining chromosome in many species, since it is the presence or absence of Y that determines the male or female sex of offspring produced in sexual reproduction. In mammals, the Y chromosome contains the gene SRY, which triggers male development. The DNA in the human Y chromosome is composed of about 62 million base pairs, making it similar in size to chromosome 19.
DNA sequencingDNA sequencing is the process of determining the nucleic acid sequence – the order of nucleotides in DNA. It includes any method or technology that is used to determine the order of the four bases: adenine, guanine, cytosine, and thymine. The advent of rapid DNA sequencing methods has greatly accelerated biological and medical research and discovery. Knowledge of DNA sequences has become indispensable for basic biological research, DNA Genographic Projects and in numerous applied fields such as medical diagnosis, biotechnology, forensic biology, virology and biological systematics.
Chromosome 7Chromosome 7 is one of the 23 pairs of chromosomes in humans, who normally have two copies of this chromosome. Chromosome 7 spans about 160 million base pairs (the building material of DNA) and represents between 5 and 5.5 percent of the total DNA in cells. The following are some of the gene count estimates of human chromosome 7. Because researchers use different approaches to genome annotation their predictions of the number of genes on each chromosome varies (for technical details, see gene prediction).
Gabor waveletGabor wavelets are wavelets invented by Dennis Gabor using complex functions constructed to serve as a basis for Fourier transforms in information theory applications. They are very similar to Morlet wavelets. They are also closely related to Gabor filters. The important property of the wavelet is that it minimizes the product of its standard deviations in the time and frequency domain. Put another way, the uncertainty in information carried by this wavelet is minimized.
DNA repairDNA repair is a collection of processes by which a cell identifies and corrects damage to the DNA molecules that encode its genome. In human cells, both normal metabolic activities and environmental factors such as radiation can cause DNA damage, resulting in tens of thousands of individual molecular lesions per cell per day. Many of these lesions cause structural damage to the DNA molecule and can alter or eliminate the cell's ability to transcribe the gene that the affected DNA encodes.
MicrosatelliteA microsatellite is a tract of repetitive DNA in which certain DNA motifs (ranging in length from one to six or more base pairs) are repeated, typically 5–50 times. Microsatellites occur at thousands of locations within an organism's genome. They have a higher mutation rate than other areas of DNA leading to high genetic diversity. Microsatellites are often referred to as short tandem repeats (STRs) by forensic geneticists and in genetic genealogy, or as simple sequence repeats (SSRs) by plant geneticists.
