11,318 research outputs found
Recommended from our members
Structure identification in relational data
This paper presents several investigations into the prospects for identifying meaningful structures in empirical data, namely, structures permitting effective organization of the data to meet requirements of future queries. We propose a general framework whereby the notion of identifiability is given a precise formal definition similar to that of learnability. Using this framework, we then explore if a tractable procedure exists for deciding whether a given relation is decomposable into a constraint network or a CNF theory with desirable topology and, if the answer is positive, identifying the desired decomposition. Finally, we address the problem of expressing a given relation as a Horn theory and, if this is impossible, finding the best k-Horn approximation to the given relation. We show that both problems can be solved in time polynomial in the length of the data
On the Usability of Probably Approximately Correct Implication Bases
We revisit the notion of probably approximately correct implication bases
from the literature and present a first formulation in the language of formal
concept analysis, with the goal to investigate whether such bases represent a
suitable substitute for exact implication bases in practical use-cases. To this
end, we quantitatively examine the behavior of probably approximately correct
implication bases on artificial and real-world data sets and compare their
precision and recall with respect to their corresponding exact implication
bases. Using a small example, we also provide qualitative insight that
implications from probably approximately correct bases can still represent
meaningful knowledge from a given data set.Comment: 17 pages, 8 figures; typos added, corrected x-label on graph
On the optimal contact potential of proteins
We analytically derive the lower bound of the total conformational energy of
a protein structure by assuming that the total conformational energy is well
approximated by the sum of sequence-dependent pairwise contact energies. The
condition for the native structure achieving the lower bound leads to the
contact energy matrix that is a scalar multiple of the native contact matrix,
i.e., the so-called Go potential. We also derive spectral relations between
contact matrix and energy matrix, and approximations related to one-dimensional
protein structures. Implications for protein structure prediction are
discussed.Comment: 5 pages, text onl
The Kinetic Energy of Hydrocarbons as a Function of Electron Density and Convolutional Neural Networks
We demonstrate a convolutional neural network trained to reproduce the
Kohn-Sham kinetic energy of hydrocarbons from electron density. The output of
the network is used as a non-local correction to the conventional local and
semi-local kinetic functionals. We show that this approximation qualitatively
reproduces Kohn-Sham potential energy surfaces when used with conventional
exchange correlation functionals. Numerical noise inherited from the
non-linearity of the neural network is identified as the major challenge for
the model. Finally we examine the features in the density learned by the neural
network to anticipate the prospects of generalizing these models
- …