162 research outputs found
Measures of greatness: A Lotkaian approach to literary authors using OCLC WorldCat
This study examines the productivity, eminence, and impact of literary authors using Lotka\u27s law, a bibliometric approach developed for studying the published output of scientists. Data on literary authors were drawn from two recent surveys that identified and ranked authors who had made the greatest contributions to world lit- erature. Data on the number of records of works by and about selected authors were drawn from OCLC WorldCat in 2007 and 2014. Findings show that the distribution of literary authors followed a pattern consistent with Lotka\u27s law and show that these studies enable one to empirically test subjective rankings of eminent authors. Future examination of distribution of author productivity might include studies based on language, location, and culture
A sharp uniform bound for the distribution of sums of Bernoulli trials
In this note we establish a uniform bound for the distribution of a sum
of independent non-homogeneous Bernoulli trials.
Specifically, we prove that where
denotes the standard deviation of and is a universal
constant. We compute the best possible constant and we show
that the bound also holds for limits of sums and differences of Bernoullis,
including the Poisson laws which constitute the worst case and attain the
bound. We also investigate the optimal bounds for and fixed. An
application to estimate the rate of convergence of Mann's fixed point
iterations is presented.Comment: This paper is a revised version of a previous articl
Tur\'an numbers for -free graphs: topological obstructions and algebraic constructions
We show that every hypersurface in contains a large grid,
i.e., the set of the form , with . We use this to
deduce that the known constructions of extremal -free and
-free graphs cannot be generalized to a similar construction of
-free graphs for any . We also give new constructions of
extremal -free graphs for large .Comment: Fixed a small mistake in the application of Proposition
Unbounded Error Quantum Query Complexity
This work studies the quantum query complexity of Boolean functions in a
scenario where it is only required that the query algorithm succeeds with a
probability strictly greater than 1/2. We show that, just as in the
communication complexity model, the unbounded error quantum query complexity is
exactly half of its classical counterpart for any (partial or total) Boolean
function. Moreover, we show that the "black-box" approach to convert quantum
query algorithms into communication protocols by Buhrman-Cleve-Wigderson
[STOC'98] is optimal even in the unbounded error setting.
We also study a setting related to the unbounded error model, called the
weakly unbounded error setting, where the cost of a query algorithm is given by
q+log(1/2(p-1/2)), where q is the number of queries made and p>1/2 is the
success probability of the algorithm. In contrast to the case of communication
complexity, we show a tight Theta(log n) separation between quantum and
classical query complexity in the weakly unbounded error setting for a partial
Boolean function. We also show the asymptotic equivalence between them for some
well-studied total Boolean functions.Comment: 14 page
A Genome-Wide Analysis of Promoter-Mediated Phenotypic Noise in Escherichia coli
Gene expression is subject to random perturbations that lead to fluctuations in the rate of protein production. As a consequence, for any given protein, genetically identical organisms living in a constant environment will contain different amounts of that particular protein, resulting in different phenotypes. This phenomenon is known as “phenotypic noise.” In bacterial systems, previous studies have shown that, for specific genes, both transcriptional and translational processes affect phenotypic noise. Here, we focus on how the promoter regions of genes affect noise and ask whether levels of promoter-mediated noise are correlated with genes' functional attributes, using data for over 60% of all promoters in Escherichia coli. We find that essential genes and genes with a high degree of evolutionary conservation have promoters that confer low levels of noise. We also find that the level of noise cannot be attributed to the evolutionary time that different genes have spent in the genome of E. coli. In contrast to previous results in eukaryotes, we find no association between promoter-mediated noise and gene expression plasticity. These results are consistent with the hypothesis that, in bacteria, natural selection can act to reduce gene expression noise and that some of this noise is controlled through the sequence of the promoter region alon
The road to deterministic matrices with the restricted isometry property
The restricted isometry property (RIP) is a well-known matrix condition that
provides state-of-the-art reconstruction guarantees for compressed sensing.
While random matrices are known to satisfy this property with high probability,
deterministic constructions have found less success. In this paper, we consider
various techniques for demonstrating RIP deterministically, some popular and
some novel, and we evaluate their performance. In evaluating some techniques,
we apply random matrix theory and inadvertently find a simple alternative proof
that certain random matrices are RIP. Later, we propose a particular class of
matrices as candidates for being RIP, namely, equiangular tight frames (ETFs).
Using the known correspondence between real ETFs and strongly regular graphs,
we investigate certain combinatorial implications of a real ETF being RIP.
Specifically, we give probabilistic intuition for a new bound on the clique
number of Paley graphs of prime order, and we conjecture that the corresponding
ETFs are RIP in a manner similar to random matrices.Comment: 24 page
Modeling recursive RNA interference.
An important application of the RNA interference (RNAi) pathway is its use as a small RNA-based regulatory system commonly exploited to suppress expression of target genes to test their function in vivo. In several published experiments, RNAi has been used to inactivate components of the RNAi pathway itself, a procedure termed recursive RNAi in this report. The theoretical basis of recursive RNAi is unclear since the procedure could potentially be self-defeating, and in practice the effectiveness of recursive RNAi in published experiments is highly variable. A mathematical model for recursive RNAi was developed and used to investigate the range of conditions under which the procedure should be effective. The model predicts that the effectiveness of recursive RNAi is strongly dependent on the efficacy of RNAi at knocking down target gene expression. This efficacy is known to vary highly between different cell types, and comparison of the model predictions to published experimental data suggests that variation in RNAi efficacy may be the main cause of discrepancies between published recursive RNAi experiments in different organisms. The model suggests potential ways to optimize the effectiveness of recursive RNAi both for screening of RNAi components as well as for improved temporal control of gene expression in switch off-switch on experiments
Deterministic and stochastic descriptions of gene expression dynamics
A key goal of systems biology is the predictive mathematical description of
gene regulatory circuits. Different approaches are used such as deterministic
and stochastic models, models that describe cell growth and division explicitly
or implicitly etc. Here we consider simple systems of unregulated
(constitutive) gene expression and compare different mathematical descriptions
systematically to obtain insight into the errors that are introduced by various
common approximations such as describing cell growth and division by an
effective protein degradation term. In particular, we show that the population
average of protein content of a cell exhibits a subtle dependence on the
dynamics of growth and division, the specific model for volume growth and the
age structure of the population. Nevertheless, the error made by models with
implicit cell growth and division is quite small. Furthermore, we compare
various models that are partially stochastic to investigate the impact of
different sources of (intrinsic) noise. This comparison indicates that
different sources of noise (protein synthesis, partitioning in cell division)
contribute comparable amounts of noise if protein synthesis is not or only
weakly bursty. If protein synthesis is very bursty, the burstiness is the
dominant noise source, independent of other details of the model. Finally, we
discuss two sources of extrinsic noise: cell-to-cell variations in protein
content due to cells being at different stages in the division cycles, which we
show to be small (for the protein concentration and, surprisingly, also for the
protein copy number per cell) and fluctuations in the growth rate, which can
have a significant impact.Comment: 23 pages, 5 figures; Journal of Statistical physics (2012
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