Rubella (German measles or 3-day measles) was officially proclaimed eliminated from the United States in 2004, largely due to intense vaccination efforts; with <10 cases reported per year, these are often travel associated and sporadic. Serologic testing for detection of antirubella antibodies can be used to establish immunity or to provide laboratory-based evidence for rubella infection ( Table 57 ). The presence of IgG antibodies to rubella virus in an asymptomatic individual indicates lifelong immunity to infection. Acute rubella infection can be serologically confirmed by documenting seroconversion to IgM and/or IgG positivity or a 4-fold rise in antirubella IgG titers between acute and convalescent serum specimens. As with measles and mumps serologic assays, however, assays providing quantitative titers for antibodies to rubella are not commonly offered at local or reference laboratories.
Laboratory Diagnosis of Rubella
Abbreviations: NAAT, nucleic acid amplification test; RT, room temperature; SST, serum separator tube.
Laboratory Diagnosis of Rubella
Abbreviations: NAAT, nucleic acid amplification test; RT, room temperature; SST, serum separator tube.
Only approximately 50% of patients are positive for IgM antibodies to rubella at the time of rash onset, which emphasizes the importance of collecting a convalescent sample. Acute phase serum should be collected upon patient presentation and again 14–21 days (minimum of 7) days later. Due to the rarity of rubella in the United States and thus the low pretest probability of infection, serologic evaluation should only be performed in patients with appropriate exposure risks and a clinical presentation highly suggestive of acute rubella; in patients not meeting these criteria, positive rubella IgM results should be interpreted with caution as they may be falsely positive.
Congenital rubella syndrome can be diagnosed by the presence of IgM-class antibodies to rubella in a neonate, alongside symptoms consistent with congenital rubella syndrome, appropriate exposure history of the mother, and lack of maternal protective immunity. NAAT for detection of rubella RNA can be performed on throat or nasal swabs and urine, though such testing is largely limited to public health laboratories and/or the CDC. Specimens for NAAT should be collected within 7 days of presentation to enhance sensitivity.
BK virus is a polyomavirus that may cause allograft nephropathy in renal transplant recipients and hemorrhagic cystitis, especially in bone marrow transplant patients. A definitive diagnosis of these conditions requires renal allograft biopsy with in situ hybridization for BK virus.
Detection of BK virus by NAAT in plasma may provide an early indication of allograft nephropathy, although there are currently no FDA-cleared NAATs ( Table 58 ) [ 276 ]. Urine cytology or quantitative NAAT may be used as a screening test, and if positive, may be followed by BK viral load testing of plasma, which has a higher clinical specificity. As there are no FDA-cleared quantitative NAATs available for monitoring BK viral loads, each institution must establish a threshold for identifying patients at highest risk of BK virus–associated nephropathy. Urine NAATs for BK virus may be more sensitive than detection of decoy cells (virus-infected cells shed from the tubules or urinary tract epithelium) using urine cytology, as BK virus DNA is typically detectable earlier in the urine than are decoy cells. However, shedding of BK virus in urine is common. Therefore, if used as a screening test, only high levels (ie, above a laboratory-established threshold that correlates with disease) should be considered significant. Urine testing for BK virus places the laboratory at risk for specimen cross-contamination, as extremely high levels of virus in the urine may lead to carryover between specimens and, potentially, false-positive results.
We have calculated the E-values implicitly used for several alignments in the UCSC genome database [ 7 ] (Additional file 1 , Table S1). They vary between 5e-10 (human/chicken) and 14000 (/). Often, higher E-value thresholds are used for genome alignment than would commonly be used for database searches (e.g. BLAST). This is reasonable because genome comparison produces many thousands of local alignments, and a few hundred or even a few thousand spurious alignments would only amount to a small fraction of these.
There is a general awareness that repeat-masking is important for genome alignment, but the efficacy of repeat-masking methods has not been assessed in this context. "Repeats" can be categorized into two types: simple (low entropy) sequences such as ATATATATAT, and non-simple repeats such as elements. Simple repeats cause spurious (i.e. non-homologous) alignments with high scores, but non-simple repeats do not, because e.g. every is genuinely homologous to every other . Non-simple repeats cause a different problem: too many alignments. In pursuit of accurate (homologous) alignment, we focus on simple repeats.
Many BLAST-like alignment tools have a capability known as "soft masking". This means that masking is applied for the first phase of the algorithm, when initial matches are found, but not for the second phase, when alignments are extended from the initial matches. This promises the best of both worlds: avoid purely repetitive alignments, but allow repeats within larger alignments.
The scoring matrix specifies a score for aligning every kind of base with every other kind of base. The simplest scoring matrix, which is actually quite good for DNA, is: +1 for all matches and -1 for all mismatches. Given a set of trusted alignments, a scoring matrix is often derived using log likelihood ratios [
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]. This is because, under simplifying independence assumptions, log likelihood ratio derived scores are theoretically optimal for discriminating between random and true alignments [
9
]. Unfortunately, real pairs of homologous sequences vary greatly in composition, and even more in conservation level; which means that the optimal matrix varies as well. To deal with this, matrices are sometimes constructed from alignments with low percent-identity, under the assumption that high percent-identity alignments will be found anyway [
8
]. Such matrices, however, will be worse at discriminating short alignments with high percent-identity from chance similarities [
10
,
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]. Another approach is to develop a small number of compromise matrices that cover a range of percent-identities close-to-optimally [
10
,
11
]. A deeper problem is that, while log likelihood scores are optimal at distinguishing true from chance similarities (i.e. alignment-level accuracy), they are not necessarily optimal for accurate base-level alignment. Thus, although log likelihood ratios are useful to suggest features of scoring matrices, it is not self-evident that they will work best in practice. (For similar reasons, the Baum-Welch training algorithm [
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] does not necessarily yield optimal alignment parameters for base-level accuracy.)
Below are some common time complexities with simple definitions. Feel free to check out Wikipedia , though, for more in-depth definitions.
Simple example with code -
So scenario on time complexity for this above given example would be -
Asymptotic Notations are languages that allow us to analyze an algorithm’s running time by identifying its behavior as the input size for the algorithm increases. This is also known as an algorithm’s growth rate.
Asymptotic NotationsThe following 3 asymptotic notations are mostly used to represent time complexity of algorithms:
Big Oh is often used to describe the worst-case of an algorithm by taking the highest order of a polynomial function and ignoring all the constants value since they aren’t too influential for sufficiently large input.
Big Omega is the opposite of Big Oh, if Big Oh was used to describe the upper bound (worst-case) of a asymptotic function, Big Omega is used to describe the lower bound of a asymptotic function. In analysis algorithm, this notation is usually used to describe the complexity of an algorithm in the best-case, which means the algorithm will not be better than its best-case .
best-caseWhen an algorithm has a complexity with lower bound = upper bound, say that an algorithm has a complexity O(n log n) and Ω(n log n), it’s actually has the complexity Θ(n log n), which means the running time of that algorithm always falls in n log n in the best-case and worst-case.
If you want to dive deep into time complexity, then refer Michael Olorunnisola ‘s article:
or look at Shilpa Jain ‘s article —
Space complexity deals with finding out how much (extra)space would be required by the algorithm with change in the input size. For e.g. it considers criteria of a data structure used in algorithm as Array or linked list.
Space complexity linked list.
How to calculate space complexity of an algorithm
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I’ll cover up at least 2 practically used algorithms in each category based on searching and sorting. I had written pseudocode and explanation in my personal notes(images here).
Search algorithms form an important part of many programs. Some searches involve looking for an entry in a database, such as looking up your record in the IRS database. Other search algorithms trawl through a virtual space, such as those hunting for the best chess moves. Although programmers can choose from numerous search types, they select the algorithm that best matches the size and structure of the database to provide a user-friendly experience.
The general searching problem can be described as follows: Locate an element in a list of distinct elements or determine that it is not in the list. The solution to this search problem is the location of the term in the list that equals and is 0 if is not in the list.
The linear search is the algorithm of choice for short lists, because it’s simple and requires minimal code to implement. The linear search algorithm looks at the first list item to see whether you are searching for it and, if so, you are finished. If not, it looks at the next item and on through each entry in the list.
Linear search is the basic search algorithm used in data structures. It is also called as sequential search. Linear search is used to find a particular element in an array. It is not compulsory to arrange an array in any order (Ascending or Descending) as in the case of binary search.
Given a sample array as shown in figure and value we want to search for is 7, then it’ll traverse in linear way.
Here is the pseudocode as divided into two images -
Linear search is rarely used practically because other search algorithms such as the binary search algorithm and hash tables allow significantly faster searching comparison to Linear search.
The time complexity of above algorithm is O(n).
Simple code in python -
Binary Search is one of the most fundamental and useful algorithms in Computer Science. It describes the process of searching for a specific value in an ordered collection.
Binary search is a popular algorithm for large databases with records ordered by numerical key. Example candidates include the IRS database keyed by social security number and the DMV records keyed by driver’s license numbers. The algorithm starts at the middle of the database — if your target number is greater than the middle number, the search will continue with the upper half of the database. If your target number is smaller than the middle number, the search will continue with the lower half of the database. It keeps repeating this process, cutting the database in half each time until it finds the record. This search is more complicated than the linear search but for large databases it’s much faster than a linear search.
Binary Search is generally composed of 3 main sections:
In its simplest form, Binary Search operates on a contiguous sequence with a specified left and right index. This is called the Search Space. Binary Search maintains the left, right, and middle indices of the search space and compares the search target or applies the search condition to the middle value of the collection; if the condition is unsatisfied or values unequal, the half in which the target cannot lie is eliminated and the search continues on the remaining half until it is successful. If the search ends with an empty half, the condition cannot be fulfilled and target is not found.
Given a sample array, first we find out midpoint and split it out. If midpoint is the search value, then it’s game over. So O(1) time complexity is achieved.
But if it’s not the midpoint’s value, then we have to go on an enchanted search for the value in divided halves. Because of this, now we can achieve time complexity in order of or i.e. O(logn) or O(n).
You can see here in above example that was found after so much of divisions of a single array(lists in python).
There are two pesudocodes possible for this algorithm. 1. Iterative 2. Recursive.
You can find difference between iteration and recursion as part of debates in reddit or stackoverflow .
The time complexity of Binary Search can be written as
Binary search implementation in python -
Illegitimate recombination has been defined as exchanges between sequences with little or no similarity, whether or not they lead to duplication or some other rearrangement type. Hideo Ikeda and coworkers have measured such exchanges using a sensitive assay in which a λ prophage in the chromosome generates specialized transducing phages ( Ikeda et al. 1995 ). Exchanges between one site within the prophage and a second site in the neighboring region of the chromosome excise a phage genome that lacks some phage genes and acquires some bacterial genes. These events have been placed into two classes. (1) Microhomology-independent events are thought to result from errors of topoisomerase and gyrase ( Ashizawa et al. 1999 ). Gyrase-mediated exchanges might also contribute to the REP-mediated events described above because gyrase has been found to cause recombination in vitro and in vivo ( Naito et al. 1984 ) and is known to bind to REP sequences ( Yang and Ames 1988 ). (2) Microhomology-dependent events are attributed to single-strand annealing because they are stimulated by the RecE and RecT proteins of the Rac prophage ( Shiraishi et al. 2006 ). At a double-strand end, RecE digests 5′ ends to reveal single-strand 3′ overhangs that are available for pairing catalyzed by the RecT protein. Given the sensitivity of these assays and their association with phage growth, it is not clear how heavily these pathways contribute to gene duplication in the bacterial chromosome. The events described by Ikeda and coworkers could also involve processes, such as template switching or TID modification as described below.
This model produces duplications within a single chromosome without need for any genetic exchange between sister chromosomes (
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). The basic TID unit is actually a triplication of a region with copies in alternating orientation (head-to-head, tail-to-tail), whose formation is thought to be initiated at quasipalindromic sequences. A symmetrical TID is diagrammed in
Figure 6
. Two mechanisms have been suggested to explain TID formation and are outlined below. Once the basic TID is formed, it can amplify by recombinational exchanges between the direct-order repeats that flank the central inverse-order copy, much like the amplification drawn for standard tandem duplications in
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B. Rearrangements of this type have been seen in two situations.
Formation of a tandem inversion duplication (TID). This model proposes initiation of duplication by one palindromic sequence at which a 3′ end can snap back to prime repair synthesis. Template switching to the opposite strand by this replication track would be aided by a second palindrome or closely placed inverse repeat. Resolution or replication leaves three copies of the intervening region—two copies in direct order with a central third copy in inverse order. This same process can in principle operate at a single-strand nick far from a replication fork. The product is a symmetrical TID (sTID) whose two junctions have short parental palindromes that have been extended in the sTID and may be prone to remodeling by deletion (
Kugelberg et al. 2010
). It is proposed that observed asymmetric join points form when deletions remove the initial palindrome and leave an asymmetric join point generated at the site of the deletion. A single large deletion that removes both junctions and the central inverse-order copy can generate a simple-tandem repeat with a short-junction (SJ) sequence. Another model achieves the same end point by template switching across two diverging replication forks (
Brewer et al. 2011
). The same structures can be explained by the microhomology-mediated break-induced replication (MMBIR) model described below (
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) in which template switches are not restricted to replication fork regions.
The simplest example is a TID amplification found in yeast after 300 generations of growth under selection for increased dosage of a sulfate transporter ( Araya et al. 2010 ). The rearrangement has five tandem copies of the same chromosomal region in alternating orientations. The basic TID has two junction types, one between head-to-head copies and another between tail-to-tail copies. Each junction has a short quasipalindromic sequence that was present in the parent chromosome (see Fig. 6 ). In the symmetrical TID, these palindromes are extended through the entire inverse-order repeat. Two models to explain the origin of the TID are outlined below. In this yeast example, the initial symmetrical TID was presumably amplified further by subsequent recombination between direct-order repeats within the TID.