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fix: remove \operatorname
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README.md

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@@ -537,13 +537,12 @@ database executes a lookup operation, any Bloom filter query that
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returns a false positive causes the database to unnecessarily read a run
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from disk. The probabliliy of these spurious reads follow a [binomial
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distribution](https://en.wikipedia.org/wiki/Binomial_distribution "https://en.wikipedia.org/wiki/Binomial_distribution")
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$`\operatorname{Binomial}(r,\operatorname{FPR})`$ where $`r`$ refers to
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the number of runs and $`\operatorname{FPR}`$ refers to the
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false-positive rate of the Bloom filters. Hence, the expected number of
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spurious reads for each lookup operation is
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$`r\cdot\operatorname{FPR}`$. The number of runs $`r`$ is proportional
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to the number of physical entries in the table. Its exact value depends
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on the merge policy of the table:
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$`\text{Binomial}(r,\text{FPR})`$ where $`r`$ refers to the number of
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runs and $`\text{FPR}`$ refers to the false-positive rate of the Bloom
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filters. Hence, the expected number of spurious reads for each lookup
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operation is $`r\cdot\text{FPR}`$. The number of runs $`r`$ is
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proportional to the number of physical entries in the table. Its exact
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value depends on the merge policy of the table:
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`LazyLevelling`
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$`r = T (\log_T\frac{n}{B} - 1) + 1`$.
@@ -578,9 +577,9 @@ $`[1\mathrm{e}{ -5 },1\mathrm{e}{ -2 }]`$.
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The total in-memory size of all Bloom filters scales *linearly* with the
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number of physical entries in the table and is determined by the number
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of physical entries multiplied by the number of bits per physical entry,
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i.e, $`n\cdot\operatorname{BPE}`$. Let us consider a table with 100
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million physical entries which uses the default table configuration for
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every parameter other than the Bloom filter size.
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i.e, $`n\cdot\text{BPE}`$. Let us consider a table with 100 million
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physical entries which uses the default table configuration for every
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parameter other than the Bloom filter size.
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| False-positive rate (FPR) | Bloom filter size | Expected spurious reads per lookup |
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|----|----|----|

lsm-tree.cabal

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@@ -335,9 +335,9 @@ description:
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Querying a Bloom filter returns either \"maybe\" meaning the key is possibly in the run or \"no\" meaning the key is definitely not in the run.
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When a query returns \"maybe\" while the key is /not/ in the run, this is referred to as a /false positive/.
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While the database executes a lookup operation, any Bloom filter query that returns a false positive causes the database to unnecessarily read a run from disk.
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The probabliliy of these spurious reads follow a [binomial distribution](https://en.wikipedia.org/wiki/Binomial_distribution) \(\operatorname{Binomial}(r,\operatorname{FPR})\)
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where \(r\) refers to the number of runs and \(\operatorname{FPR}\) refers to the false-positive rate of the Bloom filters.
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Hence, the expected number of spurious reads for each lookup operation is \(r\cdot\operatorname{FPR}\).
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The probabliliy of these spurious reads follow a [binomial distribution](https://en.wikipedia.org/wiki/Binomial_distribution) \(\text{Binomial}(r,\text{FPR})\)
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where \(r\) refers to the number of runs and \(\text{FPR}\) refers to the false-positive rate of the Bloom filters.
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Hence, the expected number of spurious reads for each lookup operation is \(r\cdot\text{FPR}\).
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The number of runs \(r\) is proportional to the number of physical entries in the table. Its exact value depends on the merge policy of the table:
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[@LazyLevelling@]
@@ -373,7 +373,7 @@ description:
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The value must be in the range \((0, 1)\).
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The recommended range is \([1\mathrm{e}{ -5 },1\mathrm{e}{ -2 }]\).
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The total in-memory size of all Bloom filters scales /linearly/ with the number of physical entries in the table and is determined by the number of physical entries multiplied by the number of bits per physical entry, i.e, \(n\cdot\operatorname{BPE}\).
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The total in-memory size of all Bloom filters scales /linearly/ with the number of physical entries in the table and is determined by the number of physical entries multiplied by the number of bits per physical entry, i.e, \(n\cdot\text{BPE}\).
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Let us consider a table with 100 million physical entries which uses the default table configuration for every parameter other than the Bloom filter size.
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+---------------------------+----------------------+------------------------------------------------------------------+

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