pinecone/core-2020-05-10-deduplication huggingface dataset:
Cheminformatics Research at the Unilever Centre for Molecular Science Informatics Cambridge

The Centre for Molecular Informatics, formerly Unilever Centre for Molecular Science Informatics (UCMSI), at the University of Cambridge is a world-leading driving force in the field of cheminformatics. Since its opening in 2000 more than 300 scientific articles have fundamentally changed the field of molecular informatics. The Centre has been a key player in promoting open chemical data and semantic access. Though mainly focussing on basic research, close collaborations with industrial partners ensured real world feedback and access to high quality molecular data. A variety of tools and standard protocols have been developed and are ubiquitous in the daily practice of cheminformatics. Here, we present a retrospective of cheminformatics research performed at the UCMSI, thereby highlighting historical and recent trends in the field as well as indicating future directions.J. E. F thanks the Medical Research Council for funding (Grant Number MR/K020919/1). Furthermore, the UCMSI acknowledges all funding sources for continuous support over the past 15 years.This is the final published version. It first appeared at http://onlinelibrary.wiley.com/doi/10.1002/minf.201400166/abstract
Predicting melting points of organic molecules : applications to aqueous solubility prediction using the General Solubility Equation

In this work we make predictions of several important molecular properties of academic and industrial importance to seek answers to two questions: 1) Can we apply efficient machine learning techniques, using inexpensive descriptors, to predict melting points to a reasonable level of accuracy? 2) Can values of this level of accuracy be usefully applied to predicting aqueous solubility? We present predictions of melting points made by several novel machine learning models, previously applied to solubility prediction. Additionally, we make predictions of solubility via the General Solubility Equation (GSE) and monitor the impact of varying the logP prediction model (AlogP and XlogP) on the GSE. We note that the machine learning models presented, using a modest number of 2D descriptors, can make melting point predictions in line with the current state of the art prediction methods (RMSE ≥ 40 oC). We also find that predicted melting points, with an RMSE of tens of degrees Celsius, can be usefully applied to the GSE to yield accurate solubility predictions (log10S RMSE < 1) over a small dataset of druglike molecules.PostprintPostprintPeer reviewe
Prediction of nucleoitide binding peptides using star graph topological indices

[Abstract] The nucleotide binding proteins are involved in many important cellular processes, such as transmission of genetic information or energy transfer and storage. Therefore, the screening of new peptides for this biological function is an important research topic. The current study proposes a mixed methodology to obtain the first classification model that is able to predict new nucleotide binding peptides, using only the amino acid sequence. Thus, the methodology uses a Star graph molecular descriptor of the peptide sequences and the Machine Learning technique for the best classifier. The best model represents a Random Forest classifier based on two features of the embedded and non-embedded graphs. The performance of the model is excellent, considering similar models in the field, with an Area Under the Receiver Operating Characteristic Curve (AUROC) value of 0.938 and true positive rate (TPR) of 0.886 (test subset). The prediction of new nucleotide binding peptides with this model could be useful for drug target studies in drug development.“Galician Network for Colorectal Cancer Research (REGICC)” (Ref. R2014/039), funded by Xunta de Galicia,“Collaborative Project on Medical Informatics (CIMED)” PI13/00280, funded by the Carlos III Health Institute from the Spanish National plan for Scientific and Technical Research and Innovation 2013–2016, and the European Regional Development Funds (FEDER
A Random Forest model for predicting allosteric and functional sites on proteins

We thank the Scottish Universities Life Sciences Alliance (SULSA) for funding to JBOM and for PB’s PhD studentship under NJW’s supervision.We created a computational method to identify allosteric sites using a machine learning method trained and tested on protein structures containing bound ligand molecules. The Random Forest machine learning approach was adopted to build our three-way predictive model. Based on descriptors collated for each ligand and binding site, the classification model allows us to assign protein cavities as allosteric, regular or orthosteric, and hence to identify allosteric sites. 43 structural descriptors per complex were derived and were used to characterize individual protein-ligand binding sites belonging to the three classes, allosteric, regular and orthosteric. We carried out a separate validation on a further unseen set of protein structures containing the ligand 2-(N-cyclohexylamino) ethane sulfonic acid (CHES).PostprintPeer reviewe
Classifiers and their Metrics Quantified

その人工知能は本当に信頼できるのか？ --人工知能の性能を正確に評価する方法を開発--. 京都大学プレスリリース. 2018-03-05.Molecular modeling frequently constructs classification models for the prediction of two-class entities, such as compound bio(in)activity, chemical property (non)existence, protein (non)interaction, and so forth. The models are evaluated using well known metrics such as accuracy or true positive rates. However, these frequently used metrics applied to retrospective and/or artificially generated prediction datasets can potentially overestimate true performance in actual prospective experiments. Here, we systematically consider metric value surface generation as a consequence of data balance, and propose the computation of an inverse cumulative distribution function taken over a metric surface. The proposed distribution analysis can aid in the selection of metrics when formulating study design. In addition to theoretical analyses, a practical example in chemogenomic virtual screening highlights the care required in metric selection and interpretation
Moving gap solitons in periodic potentials

We address existence of moving gap solitons (traveling localized solutions)
in the Gross-Pitaevskii equation with a small periodic potential. Moving gap
solitons are approximated by the explicit localized solutions of the
coupled-mode system. We show however that exponentially decaying traveling
solutions of the Gross-Pitaevskii equation do not generally exist in the
presence of a periodic potential due to bounded oscillatory tails ahead and
behind the moving solitary waves. The oscillatory tails are not accounted in
the coupled-mode formalism and are estimated by using techniques of spatial
dynamics and local center-stable manifold reductions. Existence of bounded
traveling solutions of the Gross--Pitaevskii equation with a single bump
surrounded by oscillatory tails on a finite large interval of the spatial scale
is proven by using these technique. We also show generality of oscillatory
tails in other nonlinear equations with a periodic potential.Comment: 22 pages, 2 figure
On well-posedness of the Cauchy problem for MHD system in Besov spaces

This paper is devoted to the study of the Cauchy problem of incompressible
magneto-hydrodynamics system in framework of Besov spaces. In the case of
spatial dimension $n\ge 3$ we establish the global well-posedness of the Cauchy
problem of incompressible magneto-hydrodynamics system for small data and the
local one for large data in Besov space $\dot{B}^{\frac np-1}_{p,r}(\mr^n)$,
$1\le p<\infty$ and $1\le r\le\infty$. Meanwhile, we also prove the weak-strong
uniqueness of solutions with data in $\dot{B}^{\frac np-1}_{p,r}(\mr^n)\cap
L^2(\mr^n)$ for $\frac n{2p}+\frac2r>1$. In case of $n=2$, we establish the
global well-posedness of solutions for large initial data in homogeneous Besov
space $\dot{B}^{\frac2p-1}_{p,r}(\mr^2)$ for $2< p<\infty$ and $1\le r<\infty$.Comment: 23page
Formal verification of tail distribution bounds in the HOL theorem prover

Tail distribution bounds play a major role in the estimation of failure probabilities in performance and reliability analysis of systems. They are usually estimated using Markov's and Chebyshev's inequalities, which represent tail distribution bounds for a random variable in terms of its mean or variance. This paper presents the formal verification of Markov's and Chebyshev's inequalities for discrete random variables using a higher-order-logic theorem prover. The paper also provides the formal verification of mean and variance relations for some of the widely used discrete random variables, such as Uniform(m), Bernoulli(p), Geometric(p) and Binomial(m, p) random variables. This infrastructure allows us to precisely reason about the tail distribution properties and thus turns out to be quite useful for the analysis of systems used in safety-critical domains, such as space, medicine or transportation. For illustration purposes, we present the performance analysis of the coupon collector's problem, a well-known commercially used algorithm
Spectral analysis of transport equations with bounce-back boundary conditions

International audienceWe investigate the spectral properties of the time-dependent linear transport equation with bounce-back boundary conditions. A fine analysis of the spectrum of the streaming operator is given and the explicit expression of the strongly continuous streaming semigroup is derived. Next, making use of a recent result from M. Sbihi \cite{Sbihi}, we prove, via a compactness argument, that the essential spectrum of the transport semigroup and that of the streaming semigroup coincide on all $L^p$-spaces with $
Classical solvability of the relativistic Vlasov-Maxwell system with
  bounded spatial density

In (Arch. Rational. Mech. Anal 1986, 92:59-90), Glassey and Strauss showed
that if the growth in the momentum of the particles is controlled, then the
relativistic Vlasov-Maxwell system has a classical solution globally in time.
Later they proved that such control is achieved if the kinetic energy density
of the particles remains bounded for all time (Math. Meth. Appl. Sci. 1987,
9:46-52). Here, we show that the latter assumption can be weakened to the
boundedness of the spatial density.Comment: AMS-LaTeX, 9 page
3D-mappings by means of monogenic functions and their approximation

We consider quasi-conformal 3D-mappings realized by hypercomplex
di erentiable (monogenic) functions and their polynomial
approximation. Main tools are the series development
of monogenic functions in terms of hypercomplex variables
and the generalization of L. V. Kantorovich's approach for
approximating conformal mappings by powers of a small parameter.
.This work was partially supported by the R&D Unit Matematica e Aplicacoes (UIMA) of the University of Aveiro, through Portuguese Foundation for Science and Technology (FCT
Convergence analysis of a vertex-centered finite volume scheme for a copper heap leaching model

In this paper a two-dimensional solute transport model is considered to simulate the leaching of copper ore tailing\ud
using sulfuric acid as the leaching agent. The mathematical model consists in a system of differential equations: two\ud
diffusion–convection-reaction equations with Neumann boundary conditions, and one ordinary differential equation.\ud
The numerical scheme consists in a combination of finite volume and finite element methods. A Godunov scheme is\ud
used for the convection term and an P1-FEM for the diffusion term. The convergence analysis is based on standard\ud
compactness results in L2. Some numerical examples illustrate the effectiveness of the scheme
Numerical approximations for population growth model by Rational
  Chebyshev and Hermite Functions collocation approach: A comparison

This paper aims to compare rational Chebyshev (RC) and Hermite functions (HF)
collocation approach to solve the Volterra's model for population growth of a
species within a closed system. This model is a nonlinear integro-differential
equation where the integral term represents the effect of toxin. This approach
is based on orthogonal functions which will be defined. The collocation method
reduces the solution of this problem to the solution of a system of algebraic
equations. We also compare these methods with some other numerical results and
show that the present approach is applicable for solving nonlinear
integro-differential equations.Comment: 18 pages, 5 figures; Published online in the journal of "Mathematical
  Methods in the Applied Sciences
Dynamics of Correlations of Bose and Fermi Particles

We discuss the origin of the microscopic description of correlations in
quantum many-particle systems obeying Fermi-Dirac and Bose-Einstein statistics.
For correlation operators that give the alternative description of the quantum
state evolution of Bose and Fermi particles, we deduce the von Neumann
hierarchy of nonlinear equations and construct the solution of its
initial-value problem in the corresponding spaces of sequences of trace class
operators. The links of constructed solution both with the solution of the
quantum BBGKY hierarchy and with the nonlinear BBGKY hierarchy for marginal
correlation operators are discussed. The solutions of the Cauchy problems of
these hierarchies are constructed for initial data satisfying a chaos property.Comment: 30 page
Causality Analysis of Frequency Dependent Wave Attenuation

The work is inspired by thermo-and photoacoustic imaging, where recent
efforts are devoted to take into account attenuation and varying wave speed
parameters. In this paper we derive and analyze causal equations describing
propagation of attenuated pressure waves. We also review standard models, like
frequency power laws, and the thermo-viscous equation and show that they lack
causality in the parameter range relevant for biological photoacoustic imaging.
To discuss causality in mathematical rigor we use the results and concepts of
linear system theory. We present some numerical experiments, which show the
physically unmeaningful behavior of standard attenuation models, and the
realistic behavior of the novel models
The linear sampling method for the inverse electromagnetic scattering by
  a partially coated bi-periodic structure

In this paper, we consider the inverse problem of recovering a doubly
periodic Lipschitz structure through the measurement of the scattered field
above the structure produced by point sources lying above the structure. The
medium above the structure is assumed to be homogenous and lossless with a
positive dielectric coefficient. Below the structure is a perfect conductor
partially coated with a dielectric. A periodic version of the linear sampling
method is developed to reconstruct the doubly periodic structure using the near
field data. In this case, the far field equation defined on the unit ball of
R^3 is replaced by the near field equation which is a linear integral equation
of the first kind defined on a plane above the periodic surface.Comment: 16 pages, Submitted for publicatio
A Dissipative Model for Hydrogen Storage: Existence and Regularity
  Results

We prove global existence of a solution to an initial and boundary value
problem for a highly nonlinear PDE system. The problem arises from a
thermomechanical dissipative model describing hydrogen storage by use of metal
hydrides. In order to treat the model from an analytical point of view, we
formulate it as a phase transition phenomenon thanks to the introduction of a
suitable phase variable. Continuum mechanics laws lead to an evolutionary
problem involving three state variables: the temperature, the phase parameter
and the pressure. The problem thus consists of three coupled partial
differential equations combined with initial and boundary conditions. Existence
and regularity of the solutions are here investigated by means of a time
discretization-a priori estimates-passage to the limit procedure joined with
compactness and monotonicity arguments
Transient Anomaly Imaging in Visco-Elastic Media Obeying a Frequency
  Power-Law

In this work, we consider the problem of reconstructing a small anomaly in a
viscoelastic medium from wave-field measurements. We choose Szabo's model to
describe the viscoelastic properties of the medium. Expressing the ideal
elastic field without any viscous effect in terms of the measured field in a
viscous medium, we generalize the imaging procedures, such as time reversal,
Kirchhoff Imaging and Back propagation, for an ideal medium to detect an
anomaly in a visco-elastic medium from wave-field measurements
Constructing rational and multi-wave solutions to higher order NEEs via the Exp-function method

In this paper, we present an application of some known generalizations of the Exp-function method to the fifth-order Burgers and to the seventh-order Korteweg de Vries equations for the first time. The two examples show that the Exp-function method can be an effective alternative tool for explicitly constructing rational and multi-wave solutions with arbitrary parameters to higher order nonlinear evolution equations. Being straightforward and concise, as pointed out previously, this procedure does not require the bilinear representation of the equation considered
Spectral approach to homogenization of an elliptic operator periodic in
  some directions

The operator \[ A_{\varepsilon}= D_{1} g_{1}(x_{1}/\varepsilon, x_{2}) D_{1}
+ D_{2} g_{2}(x_{1}/\varepsilon, x_{2}) D_{2} \] is considered in
$L_{2}({\mathbb{R}}^{2})$, where $g_{j}(x_{1},x_{2})$, $j=1,2,$ are periodic in
$x_{1}$ with period 1, bounded and positive definite. Let function
$Q(x_{1},x_{2})$ be bounded, positive definite and periodic in $x_{1}$ with
period 1. Let $Q^{\varepsilon}(x_{1},x_{2})= Q(x_{1}/\varepsilon, x_{2})$. The
behavior of the operator $(A_{\varepsilon}+ Q^{\varepsilon}%)^{-1}$ as
$\varepsilon\to0$ is studied. It is proved that the operator $(A_{\varepsilon}+
Q^{\varepsilon})^{-1}$ tends to $(A^{0} + Q^{0})^{-1}$ in the operator norm in
$L_{2}(\mathbb{R}^{2})$. Here $A^{0}$ is the effective operator whose
coefficients depend only on $x_{2}$, $Q^{0}$ is the mean value of $Q$ in
$x_{1}$. A sharp order estimate for the norm of the difference
$(A_{\varepsilon}+ Q^{\varepsilon})^{-1}- (A^{0} + Q^{0})^{-1}$ is obtained.
The result is applied to homogenization of the Schr\"odinger operator with a
singular potential periodic in one direction.Comment: 3
Phase Transitions for Belousov-Zhabotinsky Reactions

The main objective of this article is to study the dynamic phase transitions
associated with the spatial-temporal oscillations of the BZ reactions, given by
Field, Koros and Noyes, also referred as the Oregonator. Two criteria are
derived to determine 1) existence of either multiple equilibria or
spatiotemporal oscillations, and 2) the types of transitions. These criteria
gives a complete characterization of the dynamic transitions of the BZ systems
from the homogeneous states. The analysis is carried out using a dynamic
transition theory developed recently by the authors, which has been
successfully applied to a number of problems in science
Mechanics of Systems of Affine Bodies. Geometric Foundations and
  Applications in Dynamics of Structured Media

In the present paper we investigate the mechanics of systems of
affinely-rigid bodies, i.e., bodies rigid in the sense of affine geometry.
Certain physical applications are possible in modelling of molecular crystals,
granular media, and other physical objects. Particularly interesting are
dynamical models invariant under the group underlying geometry of degrees of
freedom. In contrary to the single body case there exist nontrivial potentials
invariant under this group (left and right acting). The concept of relative
(mutual) deformation tensors of pairs of affine bodies is discussed. Scalar
invariants built of such tensors are constructed. There is an essential novelty
in comparison to deformation scalars of single affine bodies, i.e., there exist
affinely-invariant scalars of mutual deformations. Hence, the hierarchy of
interaction models according to their invariance group, from Euclidean to
affine ones, can be considered.Comment: 50 pages, 4 figure
(Discrete) Almansi Type Decompositions: An umbral calculus framework
  based on $\mathfrak{osp}(1|2)$ symmetries

We introduce the umbral calculus formalism for hypercomplex variables
starting from the fact that the algebra of multivariate polynomials
$\BR[\underline{x}]$ shall be described in terms of the generators of the
Weyl-Heisenberg algebra. The extension of $\BR[\underline{x}]$ to the algebra
of Clifford-valued polynomials $\mathcal{P}$ gives rise to an algebra of
Clifford-valued operators whose canonical generators are isomorphic to the
orthosymplectic Lie algebra $\mathfrak{osp}(1|2)$.
  This extension provides an effective framework in continuity and discreteness
that allow us to establish an alternative formulation of Almansi decomposition
in Clifford analysis (c.f. \cite{Ryan90,MR02,MAGU}) that corresponds to a
meaningful generalization of Fischer decomposition for the subspaces $\ker
(D')^k$.
  We will discuss afterwards how the symmetries of $\mathfrak{sl}_2(\BR)$ (even
part of $\mathfrak{osp}(1|2)$) are ubiquitous on the recent approach of
\textsc{Render} (c.f. \cite{Render08}), showing that they can be interpreted in
terms of the method of separation of variables for the Hamiltonian operator in
quantum mechanics.Comment: Improved version of the Technical Report arXiv:0901.4691v1; accepted
  for publication @ Math. Meth. Appl. Sci
  http://www.mat.uc.pt/preprints/ps/p1054.pdf (Preliminary Report December
  2010
A singularly perturbed Dirichlet problem for the Laplace operator in a
  periodically perforated domain. A functional analytic approach

Let $\Omega$ be a sufficiently regular bounded open connected subset of
$\mathbb{R}^n$ such that $0 \in \Omega$ and that $\mathbb{R}^n \setminus
\mathrm{cl}\Omega$ is connected. Then we take $q_{11},..., q_{nn}\in
]0,+\infty[$ and $p \in Q\equiv \prod_{j=1}^{n}]0,q_{jj}[$. If $\epsilon$ is a
small positive number, then we define the periodically perforated domain
$\mathbb{S}[\Omega_\epsilon]^{-} \equiv \mathbb{R}^n\setminus \cup_{z \in
\mathbb{Z}^n}\mathrm{cl}\bigl(p+\epsilon \Omega +\sum_{j=1}^n
(q_{jj}z_j)e_j\bigr)$, where $\{e_1,...,e_n\}$ is the canonical basis of
$\mathbb{R}^n$. For $\epsilon$ small and positive, we introduce a particular
Dirichlet problem for the Laplace operator in the set
$\mathbb{S}[\Omega_\epsilon]^{-}$. Namely, we consider a Dirichlet condition on
the boundary of the set $p+\epsilon \Omega$, together with a periodicity
condition. Then we show real analytic continuation properties of the solution
and of the corresponding energy integral as functionals of the pair of
$\epsilon$ and of the Dirichlet datum on $p+\epsilon \partial \Omega$, around a
degenerate pair with $\epsilon=0$
Some exact solutions for Toda type lattice differential equations using the improved (G′/G)-expansion method

Nonlinear lattice differential equations (also known as differential-difference equations) appear in many applications. They can be thought of as hybrid systems for the inclusion of both discrete and continuous variables. On the basis of an improved version of the basic (G′/G)- expansion method, we focus our attention towards some Toda type lattice differential systems for constructing further exact traveling wave solutions. Our method provides not only solitary and periodic wave profiles but also rational solutions with more arbitrary parameters. © 2012 John Wiley & Sons, Ltd