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+@Article{boecker08decomp, 

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+author = {Sebastian B\"ocker and Zsuzsanna Lipt\'ak and Marcel Martin and Anton Pervukhin and Henner Sudek}, 

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+title = {{DECOMP}from interpreting Mass Spectrometry peaks to solving the {Money} {Changing} {Problem}}, 

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+journal = {Bioinformatics}, 

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+year = {2008}, 

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+volume = {24}, 

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+number = {4}, 

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+pages = {591593}, 

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+url = {http://bioinformatics.oxfordjournals.org/cgi/reprint/24/4/591?ijkey=1lM50Bkzz4SCLsa&keytype=ref}, 

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+doi = {10.1093/bioinformatics/btm631}, 

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+abstract = {We introduce DECOMP, a tool that computes the sum formula 

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+ of all molecules whose mass equals the input 

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+ mass. This problem arises frequently in biochemistry 

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+ and mass spectrometry (MS), when we know the 

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+ molecular mass of a protein, DNA, or metabolite 

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+ fragment but have no other information. A closely 

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+ related problem is known as the Money Changing 

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+ Problem (MCP), where all masses are positive 

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+ integers. Recently, efficient algorithms have been 

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+ developed for the MCP, which DECOMP applies to real 

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+ valued MS data. The excellent performance of this 

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+ method on proteomic and metabolomic MS data has 

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+ recently been demonstrated. DECOMP has an 

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+ easytouse graphical interface, which caters for 

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+ both types of users: those interested in solving MCP 

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+ instances and those submitting MS data.}, 

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+} 

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+ 

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+@Article{boecker09sirius, 

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+author = {Sebastian B\"ocker and Matthias Letzel and Zsuzsanna Lipt{\'a}k and Anton Pervukhin}, 

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+title = {{SIRIUS}: Decomposing isotope patterns for metabolite identification}, 

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+journal = {Bioinformatics}, 

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+year = {2009}, 

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+volume = {25}, 

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+number = {2}, 

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+pages = {218224}, 

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+url = {http://bioinformatics.oxfordjournals.org/cgi/content/full/25/2/218}, 

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+doi = {10.1093/bioinformatics/btn603}, 

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+abstract = {Motivation: Highresolution mass spectrometry (MS) is 

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+ among the most widely used technologies in 

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+ metabolomics. Metabolites participate in almost all 

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+ cellular processes, but most metabolites still 

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+ remain uncharacterized. Determination of the sum 

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+ formula is a crucial step in the identification of 

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+ an unknown metabolite, as it reduces its possible 

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+ structures to a hopefully manageable set. Results: 

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+ We present a method for determining the sum formula 

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+ of a metabolite solely from its mass and the natural 

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+ distribution of its isotopes. Our input is a 

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+ measured isotope pattern from a high resolution mass 

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+ spectrometer, and we want to find those molecules 

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+ that best match this pattern. Our method is 

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+ computationally efficient, and results on 

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+ experimental data are very promising: For orthogonal 

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+ timeofflight mass spectrometry, we correctly 

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+ identify sum formulas for more than 90\% of the 

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+ molecules, ranging in mass up to 1000 

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+ Da. Availability: SIRIUS is available under the LGPL 

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+ license at 

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+ http://bio.informatik.unijena.de/sirius/. Contact: 

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+ anton.pervukhin@minet.unijena.de}, 

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+} 

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+ 

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+@Inproceedings{boecker06decomposing, 

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+author = {Sebastian B\"ocker and Matthias Letzel and Zsuzsanna Lipt{\'a}k and Anton Pervukhin}, 

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+title = {Decomposing metabolomic isotope patterns}, 

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+booktitle = {Proc. of Workshop on Algorithms in Bioinformatics (WABI 2006)}, 

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+publisher = {Springer, Berlin}, 

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+year = {2006}, 

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+volume = {4175}, 

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+pages = {1223}, 

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+series = {Lect. Notes Comput. Sci.}, 

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+url = {http://bio.informatik.unijena.de/bib2html/downloads/2006/BoeckerEtAl_DecomposingMetabolomicIsotopePatterns_WABI_2006.pdf}, 

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+abstract = {We present a method for determining the sum formula of 

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+ metabolites solely from their mass and isotope 

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+ pattern. Metabolites, such as sugars or lipids, 

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+ participate in almost all cellular processes, but 

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+ the majority still remains uncharacterized. Our 

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+ input is a measured isotope pattern from a high 

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+ resolution mass spectrometer, and we want to find 

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+ those molecules that best match this 

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+ pattern. Determination of the sum formula is a 

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+ crucial step in the identification of an unknown 

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+ metabolite, as it reduces its possible structures to 

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+ a hopefully manageable set. Our method is 

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+ computationally efficient, and first results on 

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+ experimental data indicate good identification rates 

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+ for chemical compounds up to 700 Dalton. Above 1000 

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+ Dalton, the number of molecules with a certain mass 

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+ increases rapidly. To efficiently analyze mass 

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+ spectra of such molecules, we define several 

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+ additive invariants extracted from the input and 

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+ then propose to solve a joint decomposition 

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+ problem.}, 

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+} 

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+ 

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+@Article{boecker07fast, 

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+author = {Sebastian B\"ocker and Zsuzsanna Lipt{\'a}k}, 

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+title = {A fast and simple algorithm for the {M}oney {C}hanging {P}roblem}, 

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+journal = {Algorithmica}, 

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+year = {2007}, 

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+volume = {48}, 

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+number = {4}, 

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+pages = {413432}, 

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+doi = {10.1007/s0045300701628}, 

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+abstract = {The Money Changing Problem (MCP) can be stated as follows: 

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+ Given $k$ positive integers $a_1< \ldots < a_k$ and 

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+ a query integer $M$, is there a linear combination 

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+ $\sum_i c_ia_i = M$ with nonnegative integers 

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+ $c_i$, a \emph{decomposition} of $M$? If so, produce 

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+ one or all such decompositions. The largest integer 

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+ without such a decomposition is called the 

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+ \emph{Frobenius number} $g(a_1,\ldots,a_k)$. A data 

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+ structure called {\em residue table} of $a_1$ words 

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+ can be used to compute the Frobenius number in time 

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+ $O(a_1)$. We present an intriguingly simple 

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+ algorithm for computing the residue table which runs 

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+ in time $O(ka_1)$, with no additional memory 

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+ requirements, outperforming the best previously 

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+ known algorithm. Simulations show that it performs 

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+ well even on 'hard' instances from the 

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+ literature. In addition, we can employ the residue 

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+ table to answer MCP decision instances in constant 

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+ time, and a slight modification of size $O(a_1)$ to 

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+ compute one decomposition for a query $M$. Note that 

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+ since both, computing the Frobenius number and MCP 

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+ (decision) are NPhard, one cannot expect to find an 

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+ algorithm that is polynomial in the size of the 

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+ input, i.e., in $k,\log a_k$, and $\log M$. We then 

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+ give an algorithm which, using a modification of the 

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+ residue table, also constructible in $O(ka_1)$ time, 

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+ computes all decompositions of a query integer 

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+ $M$. Its worstcase running time is $O(ka_1)$ for 

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+ each decomposition, thus the total runtime depends 

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+ only on the output size and is independent of the 

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+ size of query $M$ itself. We apply our latter 

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+ algorithm to interpreting mass spectrometry (MS) 

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+ peaks: Due to its high speed and accuracy, MS is now 

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+ the method of choice in protein 

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+ identification. Interpreting individual peaks is one 

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+ of the recurring subproblems in analyzing MS data; 

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+ the task is to identify sample molecules whose mass 

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+ the peak possibly represents. This can be stated as 

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+ an MCP instance, with the masses of the individual 

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+ amino acids as the $k$ integers $a_1,\ldots, 

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+ a_k$. Our simulations show that our algorithm is 

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+ fast on real data and is well suited for generating 

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+ candidates for peak interpretation.}, 

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+} 

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