Search results for "mutation."

Right-jumps and pattern avoiding permutations

2015

We study the iteration of the process "a particle jumps to the right" in permutations. We prove that the set of permutations obtained in this model after a given number of iterations from the identity is a class of pattern avoiding permutations. We characterize the elements of the basis of this class and we enumerate these "forbidden minimal patterns" by giving their bivariate exponential generating function: we achieve this via a catalytic variable, the number of left-to-right maxima. We show that this generating function is a D-finite function satisfying a nice differential equation of order~2. We give some congruence properties for the coefficients of this generating function, and we sho…

On Block Sensitivity and Fractional Block Sensitivity

2018

We investigate the relation between the block sensitivity bs(f) and fractional block sensitivity fbs(f) complexity measures of Boolean functions. While it is known that fbs(f) = O(bs(f)2), the best known separation achieves $${\rm{fbs}}\left( f \right) = \left( {{{\left( {3\sqrt 2 } \right)}^{ - 1}} + o\left( 1 \right)} \right){\rm{bs}}{\left( f \right)^{3/2}}$$ . We improve the constant factor and show a family of functions that give fbs(f) = (6−1/2 − o(1)) bs(f)3/2.

All Classical Adversary Methods Are Equivalent for Total Functions

2017

We show that all known classical adversary lower bounds on randomized query complexity are equivalent for total functions and are equal to the fractional block sensitivity fbs( f ). That includes the Kolmogorov complexity bound of Laplante and Magniez and the earlier relational adversary bound of Aaronson. This equivalence also implies that for total functions, the relational adversary is equivalent to a simpler lower bound, which we call rank-1 relational adversary. For partial functions, we show unbounded separations between fbs( f ) and other adversary bounds, as well as between the adversary bounds themselves. We also show that, for partial functions, fractional block sensitivity canno…

Quantum lower bound for inverting a permutation with advice

2014

Given a random permutation $f: [N] \to [N]$ as a black box and $y \in [N]$, we want to output $x = f^{-1}(y)$. Supplementary to our input, we are given classical advice in the form of a pre-computed data structure; this advice can depend on the permutation but \emph{not} on the input $y$. Classically, there is a data structure of size $\tilde{O}(S)$ and an algorithm that with the help of the data structure, given $f(x)$, can invert $f$ in time $\tilde{O}(T)$, for every choice of parameters $S$, $T$, such that $S\cdot T \ge N$. We prove a quantum lower bound of $T^2\cdot S \ge \tilde{\Omega}(\epsilon N)$ for quantum algorithms that invert a random permutation $f$ on an $\epsilon$ fraction of…

Mahonian STAT on words

2016

In 2000, Babson and Steingrimsson introduced the notion of what is now known as a permutation vincular pattern, and based on it they re-defined known Mahonian statistics and introduced new ones, proving or conjecturing their Mahonity. These conjectures were proved by Foata and Zeilberger in 2001, and by Foata and Randrianarivony in 2006.In 2010, Burstein refined some of these results by giving a bijection between permutations with a fixed value for the major index and those with the same value for STAT , where STAT is one of the statistics defined and proved to be Mahonian in the 2000 Babson and Steingrimsson's paper. Several other statistics are preserved as well by Burstein's bijection.At…

Sensitivity versus block sensitivity of Boolean functions

2010

Determining the maximal separation between sensitivity and block sensitivity of Boolean functions is of interest for computational complexity theory. We construct a sequence of Boolean functions with bs(f) = 1/2 s(f)^2 + 1/2 s(f). The best known separation previously was bs(f) = 1/2 s(f)^2 due to Rubinstein. We also report results of computer search for functions with at most 12 variables.

Inhibition of FTSJ1, a tryptophan tRNA-specific 2’-O-methyltransferase as possible mechanism to readthrough premature termination codons (UGAs) of th…

2022

Cystic Fibrosis (CF) is an autosomal recessive genetic disease caused by mutations in the CFTR gene, coding for the CFTR chloride channel. About 10 % of the mutations affecting the CFTR gene are "stop" mutations, which generate a Premature Termination Codon (PTC), thus resulting in the synthesis of a truncated CFTR protein. A way to bypass PTC relies on ribosome readthrough, that is the capacity of the ribosome to skip a PTC, thus generating a full-length protein. “TRIDs” are molecules exerting ribosome readthrough and for some of them the mechanism of action is still under debate. By in silico analysis as well as in vitro studies, we investigate a possible mechanism of action (MOA) by whic…

Gene symbol: f9.

2007

Confidence-based Somatic Mutation Evaluation and Prioritization

2012

Next generation sequencing (NGS) has enabled high throughput discovery of somatic mutations. Detection depends on experimental design, lab platforms, parameters and analysis algorithms. However, NGS-based somatic mutation detection is prone to erroneous calls, with reported validation rates near 54% and congruence between algorithms less than 50%. Here, we developed an algorithm to assign a single statistic, a false discovery rate (FDR), to each somatic mutation identified by NGS. This FDR confidence value accurately discriminates true mutations from erroneous calls. Using sequencing data generated from triplicate exome profiling of C57BL/6 mice and B16-F10 melanoma cells, we used the exist…

Localization of non-specific X-linked mental retardation gene (MRX73) to Xp22.2.

2001

Clinical and molecular studies are reported on a family (MRX73) of five males with non-specific X-linked mental retardation (XLMR). A total of 33 microsatellite and RFLP markers was typed. The gene for this XLMR condition was been linked to DXS1195, with a lod score of 2.36 at theta = 0. The haplotype and multipoint linkage analyses suggest localization of the MRX73 locus to an interval of 2 cM defined by markers DXS8019 and DXS365, in Xp22.2. This interval contains the gene of Coffin-Lowry syndrome (RSK2), where a missense mutation has been associated with a form of non-specific mental retardation. Therefore, a search for RSK2 mutations was performed in the MRX73 family, but no causal muta…