291 research outputs found
Improved large-scale prediction of growth inhibition patterns using the NCI60 cancer cell line panel
International audienceMotivation: Recent large-scale omics initiatives have catalogued the somatic alterations of cancer cell line panels along with their pharmacological response to hundreds of compounds. In this study, we have explored these data to advance computational approaches that enable more effective and targeted use of current and future anticancer therapeutics.Results: We modelled the 50% growth inhibition bioassay end-point (GI50) of 17 142 compounds screened against 59 cancer cell lines from the NCI60 panel (941 831 data-points, matrix 93.08% complete) by integrating the chemical and biological (cell line) information. We determine that the protein, gene transcript and miRNA abundance provide the highest predictive signal when modelling the GI50 endpoint, which significantly outperformed the DNA copy-number variation or exome sequencing data (Tukey’s Honestly Significant Difference, P <0.05). We demonstrate that, within the limits of the data, our approach exhibits the ability to both interpolate and extrapolate compound bioactivities to new cell lines and tissues and, although to a lesser extent, to dissimilar compounds. Moreover, our approach outperforms previous models generated on the GDSC dataset. Finally, we determine that in the cases investigated in more detail, the predicted drug-pathway associations and growth inhibition patterns are mostly consistent with the experimental data, which also suggests the possibility of identifying genomic markers of drug sensitivity for novel compounds on novel cell lines
Bounds on the heat kernel of the Schroedinger operator in a random electromagnetic field
We obtain lower and upper bounds on the heat kernel and Green functions of
the Schroedinger operator in a random Gaussian magnetic field and a fixed
scalar potential. We apply stochastic Feynman-Kac representation, diamagnetic
upper bounds and the Jensen inequality for the lower bound. We show that if the
covariance of the electromagnetic (vector) potential is increasing at large
distances then the lower bound is decreasing exponentially fast for large
distances and a large time.Comment: some technical improvements, new references, to appear in
Journ.Phys.
Financial correlations at ultra-high frequency: theoretical models and empirical estimation
A detailed analysis of correlation between stock returns at high frequency is
compared with simple models of random walks. We focus in particular on the
dependence of correlations on time scales - the so-called Epps effect. This
provides a characterization of stochastic models of stock price returns which
is appropriate at very high frequency.Comment: 22 pages, 8 figures, 1 table, version to appear in EPJ
The monomer-dimer problem and moment Lyapunov exponents of homogeneous Gaussian random fields
We consider an "elastic" version of the statistical mechanical monomer-dimer
problem on the n-dimensional integer lattice. Our setting includes the
classical "rigid" formulation as a special case and extends it by allowing each
dimer to consist of particles at arbitrarily distant sites of the lattice, with
the energy of interaction between the particles in a dimer depending on their
relative position. We reduce the free energy of the elastic dimer-monomer (EDM)
system per lattice site in the thermodynamic limit to the moment Lyapunov
exponent (MLE) of a homogeneous Gaussian random field (GRF) whose mean value
and covariance function are the Boltzmann factors associated with the monomer
energy and dimer potential. In particular, the classical monomer-dimer problem
becomes related to the MLE of a moving average GRF. We outline an approach to
recursive computation of the partition function for "Manhattan" EDM systems
where the dimer potential is a weighted l1-distance and the auxiliary GRF is a
Markov random field of Pickard type which behaves in space like autoregressive
processes do in time. For one-dimensional Manhattan EDM systems, we compute the
MLE of the resulting Gaussian Markov chain as the largest eigenvalue of a
compact transfer operator on a Hilbert space which is related to the
annihilation and creation operators of the quantum harmonic oscillator and also
recast it as the eigenvalue problem for a pantograph functional-differential
equation.Comment: 24 pages, 4 figures, submitted on 14 October 2011 to a special issue
of DCDS-
Chemically Aware Model Builder (camb): an R package for property and bioactivity modelling of small molecules.
BACKGROUND: In silico predictive models have proved to be valuable for the optimisation of compound potency, selectivity and safety profiles in the drug discovery process. RESULTS: camb is an R package that provides an environment for the rapid generation of quantitative Structure-Property and Structure-Activity models for small molecules (including QSAR, QSPR, QSAM, PCM) and is aimed at both advanced and beginner R users. camb's capabilities include the standardisation of chemical structure representation, computation of 905 one-dimensional and 14 fingerprint type descriptors for small molecules, 8 types of amino acid descriptors, 13 whole protein sequence descriptors, filtering methods for feature selection, generation of predictive models (using an interface to the R package caret), as well as techniques to create model ensembles using techniques from the R package caretEnsemble). Results can be visualised through high-quality, customisable plots (R package ggplot2). CONCLUSIONS: Overall, camb constitutes an open-source framework to perform the following steps: (1) compound standardisation, (2) molecular and protein descriptor calculation, (3) descriptor pre-processing and model training, visualisation and validation, and (4) bioactivity/property prediction for new molecules. camb aims to speed model generation, in order to provide reproducibility and tests of robustness. QSPR and proteochemometric case studies are included which demonstrate camb's application.Graphical abstractFrom compounds and data to models: a complete model building workflow in one package
The Beurling--Malliavin Multiplier Theorem and its analogs for the de Branges spaces
Let be a non-negative function on . We are looking for a
non-zero from a given space of entire functions satisfying The
classical Beurling--Malliavin Multiplier Theorem corresponds to and the
classical Paley--Wiener space as . We survey recent results for the case
when is a de Branges space \he. Numerous answers mainly depend on the
behaviour of the phase function of the generating function .Comment: Survey, 25 page
On the relation between standard and -symmetries for PDEs
We give a geometrical interpretation of the notion of -prolongations of
vector fields and of the related concept of -symmetry for partial
differential equations (extending to PDEs the notion of -symmetry for
ODEs). We give in particular a result concerning the relationship between
-symmetries and standard exact symmetries. The notion is also extended to
the case of conditional and partial symmetries, and we analyze the relation
between local -symmetries and nonlocal standard symmetries.Comment: 25 pages, no figures, latex. to be published in J. Phys.
Polypharmacology Modelling Using Proteochemometrics (PCM): Recent Methodological Developments, Applications to Target Families, and Future Prospects
Peer reviewe
Structural and Electronic Properties of Small Neutral (MgO)n Clusters
Ab initio Perturbed Ion (PI) calculations are reported for neutral
stoichiometric (MgO)n clusters (n<14). An extensive number of isomer structures
was identified and studied. For the isomers of (MgO)n (n<8) clusters, a full
geometrical relaxation was considered. Correlation corrections were included
for all cluster sizes using the Coulomb-Hartree-Fock (CHF) model proposed by
Clementi. The results obtained compare favorably to the experimental data and
other previous theoretical studies. Inclusion of correlaiotn is crucial in
order to achieve a good description of these systems. We find an important
number of new isomers which allows us to interpret the experimental magic
numbers without the assumption of structures based on (MgO)3 subunits. Finally,
as an electronic property, the variations in the cluster ionization potential
with the cluster size were studied and related to the structural isomer
properties.Comment: 24 pages, LaTeX, 7 figures in GIF format. Accepted for publication in
Phys. Rev.
Brownian Motions on Metric Graphs
Brownian motions on a metric graph are defined. Their generators are
characterized as Laplace operators subject to Wentzell boundary at every
vertex. Conversely, given a set of Wentzell boundary conditions at the vertices
of a metric graph, a Brownian motion is constructed pathwise on this graph so
that its generator satisfies the given boundary conditions.Comment: 43 pages, 7 figures. 2nd revision of our article 1102.4937: The
introduction has been modified, several references were added. This article
will appear in the special issue of Journal of Mathematical Physics
celebrating Elliott Lieb's 80th birthda
- …