MOTIVATION: Although many methods and statistical approaches have been developed for protein identification by mass spectrometry, the problem of accurate assessment of statistical significance of protein identifications remains an open question. The main issues are as follows: (i) statistical significance of inferring peptide from experimental mass spectra must be platform independent and spectrum specific and (ii) individual spectrum matches at the peptide level must be combined into a single statistical measure at the protein level. RESULTS: We present a method and software to assign statistical significance to protein identifications from search engines for mass spectrometric data. The approach is based on asymptotic theory of order statistics. The parameters of the asymptotic distributions of identification scores are estimated for each spectrum individually. The method relies on new unbiased estimators for parameters of extreme value distribution. The estimated parameters are used to assign a spectrum-specific P-value to each peptide-spectrum match. The protein-level confidence measure combines P-values of peptide-to-spectrum matches. CONCLUSION: We extensively tested the method using triplicate mouse and yeast high-throughput proteomic experiments. The proposed statistical approach improves the sensitivity of protein identifications without compromising specificity. While the method was primarily designed to work with Mascot, it is platform-independent and is applicable to any search engine which outputs a single score for a peptide-spectrum match. We demonstrate this by testing the method in conjunction with X!Tandem. AVAILABILITY: The software is available for download at ftp://genetics.bwh.harvard.edu/SSPV/. CONTACT: [email protected] SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

For a binary sequenceSn= {si:i=1,2,...,n} ∈ {±1}n,n> 1, the peak sidelobe level (PSL) is defined as M(Sn)=maxk=1,2,...,n-1|∑i=1n-kSiSi+k|. It is shown that the distribution ofM(Sn) is strongly concentrated, and asymptotically almost surely γ(Sn) = (M(Sn))/√(n In n) ∈ [1-o(1),√2]. Explicit bounds for the number of sequences outside this range are provided. This improves on the best earlier known result due to Moon and Moser that the typical γ(Sn) ∈ [o([1/(√(ln n))]),2], and settles to the affirmative the conjecture of Dmitriev and Jedwab on the growth rate of the typical peak sidelobe. Finally, it is shown that modulo some natural conjecture, the typical γ(Sn) equals√2.

For a binary sequence in given equation, the peak sidelobe level (PSL) is defined as by a certain equation. It is shown that the distribution of M(Sn) is strongly concentrated, and asymptotically almost surely, as per a derived equation. Explicit bounds for the number of sequences outside this range are provided. This improves on the best earlier known bounds due to Moon and Moser [1968] claiming that the typical value in equation 3 and settles to the affirmative a conjecture of Dmitriev and Jedwab [2007] on the growth rate of the typical peak sidelobe.

Nonlinearity is the number of bits which must change in the truth table of a Boolean function to reach the closest affine function. It may be expressed through the maximum of the absolute value of a component in the function's Walsh–Hadamard transform. Concentration of nonlinearity is proved. The derived bounds on the concentration point and tails of the distribution are tighter than the earlier known ones.

A relation is established between the strength of a binary code over the alphabet {+1,-1}, and its ability to reduce peak-to-mean envelope power ratio (PMEPR) in n-subcarrier (OFDM) signals. Based on this relation, a method is proposed to deterministically bound PMEPR of such signals using coordinate-wise multiplication by a balancing vector (BV) chosen from a code of given strength. A practical probabilistic scheme considering a small number of candidate codewords is devised. For this scheme, estimates on the PMEPR reduction achievable with arbitrary high probability are derived. In particular, the scheme provides for large n PMEPR of lnn+2.01lnlnn with (ln2)middot(log2n)2+1 bits of redundancy, the failure probability at most e-n, and testing n/(lnlnn) candidate BVs. Finally, several practical settings are considered. For example, for quaternary phase-shift keying, n=128, the scheme with 36 bits of redundancy (18 redundant subcarriers), by testing only 4 BVs provides over 2 dB PMEPR reduction, for any failure rate below 10-2.5