6,969 research outputs found
GTI-space : the space of generalized topological indices
A new extension of the generalized topological indices (GTI) approach is carried out torepresent 'simple' and 'composite' topological indices (TIs) in an unified way. Thisapproach defines a GTI-space from which both simple and composite TIs represent particular subspaces. Accordingly, simple TIs such as Wiener, Balaban, Zagreb, Harary and Randićconnectivity indices are expressed by means of the same GTI representation introduced for composite TIs such as hyper-Wiener, molecular topological index (MTI), Gutman index andreverse MTI. Using GTI-space approach we easily identify mathematical relations between some composite and simple indices, such as the relationship between hyper-Wiener and Wiener index and the relation between MTI and first Zagreb index. The relation of the GTI space with the sub-structural cluster expansion of property/activity is also analysed and some routes for the applications of this approach to QSPR/QSAR are also given
Blind Source Separation with Optimal Transport Non-negative Matrix Factorization
Optimal transport as a loss for machine learning optimization problems has
recently gained a lot of attention. Building upon recent advances in
computational optimal transport, we develop an optimal transport non-negative
matrix factorization (NMF) algorithm for supervised speech blind source
separation (BSS). Optimal transport allows us to design and leverage a cost
between short-time Fourier transform (STFT) spectrogram frequencies, which
takes into account how humans perceive sound. We give empirical evidence that
using our proposed optimal transport NMF leads to perceptually better results
than Euclidean NMF, for both isolated voice reconstruction and BSS tasks.
Finally, we demonstrate how to use optimal transport for cross domain sound
processing tasks, where frequencies represented in the input spectrograms may
be different from one spectrogram to another.Comment: 22 pages, 7 figures, 2 additional file
Punctuated equilibria and 1/f noise in a biological coevolution model with individual-based dynamics
We present a study by linear stability analysis and large-scale Monte Carlo
simulations of a simple model of biological coevolution. Selection is provided
through a reproduction probability that contains quenched, random interspecies
interactions, while genetic variation is provided through a low mutation rate.
Both selection and mutation act on individual organisms. Consistent with some
current theories of macroevolutionary dynamics, the model displays
intermittent, statistically self-similar behavior with punctuated equilibria.
The probability density for the lifetimes of ecological communities is well
approximated by a power law with exponent near -2, and the corresponding power
spectral densities show 1/f noise (flicker noise) over several decades. The
long-lived communities (quasi-steady states) consist of a relatively small
number of mutualistically interacting species, and they are surrounded by a
``protection zone'' of closely related genotypes that have a very low
probability of invading the resident community. The extent of the protection
zone affects the stability of the community in a way analogous to the height of
the free-energy barrier surrounding a metastable state in a physical system.
Measures of biological diversity are on average stationary with no discernible
trends, even over our very long simulation runs of approximately 3.4x10^7
generations.Comment: 20 pages RevTex. Minor revisions consistent with published versio
Probabilistic Line Searches for Stochastic Optimization
In deterministic optimization, line searches are a standard tool ensuring
stability and efficiency. Where only stochastic gradients are available, no
direct equivalent has so far been formulated, because uncertain gradients do
not allow for a strict sequence of decisions collapsing the search space. We
construct a probabilistic line search by combining the structure of existing
deterministic methods with notions from Bayesian optimization. Our method
retains a Gaussian process surrogate of the univariate optimization objective,
and uses a probabilistic belief over the Wolfe conditions to monitor the
descent. The algorithm has very low computational cost, and no user-controlled
parameters. Experiments show that it effectively removes the need to define a
learning rate for stochastic gradient descent.Comment: Extended version of the NIPS '15 conference paper, includes detailed
pseudo-code, 59 pages, 35 figure
Wiener-Type Topological Indices
A unified approach to the Wiener topological index and its various recent modifications, is presented. Among these modifications particular attention is paid to the Kirchhoff, Harary, Szeged, Cluj and Schultz indices, as well as their numerous variants and generalizations. Relations between these indices are established and methods for their computation described. Correlation of these topological indices with physico-chemical properties of molecules, as well as their mutual correlation are examined
Fables of reconstruction: controlling bias in the dark energy equation of state
We develop an efficient, non-parametric Bayesian method for reconstructing
the time evolution of the dark energy equation of state w(z) from observational
data. Of particular importance is the choice of prior, which must be chosen
carefully to minimise variance and bias in the reconstruction. Using a
principal component analysis, we show how a correlated prior can be used to
create a smooth reconstruction and also avoid bias in the mean behaviour of
w(z). We test our method using Wiener reconstructions based on Fisher matrix
projections, and also against more realistic MCMC analyses of simulated data
sets for Planck and a future space-based dark energy mission. While the
accuracy of our reconstruction depends on the smoothness of the assumed w(z),
the relative error for typical dark energy models is <10% out to redshift
z=1.5.Comment: 13 pages, 11 figure
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