On the validity of parametric block correlation matrices with constant within and between group correlations

We consider the set Bp of parametric block correlation matrices with p blocks of various (and possibly different) sizes, whose diagonal blocks are compound symmetry (CS) correlation matrices and off-diagonal blocks are constant matrices. Such matrices appear in probabilistic models on categorical data, when the levels are partitioned in p groups, assuming a constant correlation within a group and a constant correlation for each pair of groups. We obtain two necessary and sufficient conditions for positive definiteness of elements of Bp. Firstly we consider the block average map $\phi$, consisting in replacing a block by its mean value. We prove that for any A $\in$ Bp , A is positive definite if and only if $\phi$(A) is positive definite. Hence it is equivalent to check the validity of the covariance matrix of group means, which only depends on the number of groups and not on their sizes. This theorem can be extended to a wider set of block matrices. Secondly, we consider the subset of Bp for which the between group correlation is the same for all pairs of groups. Positive definiteness then comes down to find the positive definite interval of a matrix pencil on Sp. We obtain a simple characterization by localizing the roots of the determinant with within group correlation values

Multi-class protein fold classification using a new ensemble machine learning approach.

Protein structure classification represents an important process in understanding the associations between sequence and structure as well as possible functional and evolutionary relationships. Recent structural genomics initiatives and other high-throughput experiments have populated the biological databases at a rapid pace. The amount of structural data has made traditional methods such as manual inspection of the protein structure become impossible. Machine learning has been widely applied to bioinformatics and has gained a lot of success in this research area. This work proposes a novel ensemble machine learning method that improves the coverage of the classifiers under the multi-class imbalanced sample sets by integrating knowledge induced from different base classifiers, and we illustrate this idea in classifying multi-class SCOP protein fold data. We have compared our approach with PART and show that our method improves the sensitivity of the classifier in protein fold classification. Furthermore, we have extended this method to learning over multiple data types, preserving the independence of their corresponding data sources, and show that our new approach performs at least as well as the traditional technique over a single joined data source. These experimental results are encouraging, and can be applied to other bioinformatics problems similarly characterised by multi-class imbalanced data sets held in multiple data sources

Differential fast fixed-point algorithms for underdetermined instantaneous and convolutive partial blind source separation

This paper concerns underdetermined linear instantaneous and convolutive blind source separation (BSS), i.e., the case when the number of observed mixed signals is lower than the number of sources.We propose partial BSS methods, which separate supposedly nonstationary sources of interest (while keeping residual components for the other, supposedly stationary, "noise" sources). These methods are based on the general differential BSS concept that we introduced before. In the instantaneous case, the approach proposed in this paper consists of a differential extension of the FastICA method (which does not apply to underdetermined mixtures). In the convolutive case, we extend our recent time-domain fast fixed-point C-FICA algorithm to underdetermined mixtures. Both proposed approaches thus keep the attractive features of the FastICA and C-FICA methods. Our approaches are based on differential sphering processes, followed by the optimization of the differential nonnormalized kurtosis that we introduce in this paper. Experimental tests show that these differential algorithms are much more robust to noise sources than the standard FastICA and C-FICA algorithms.Comment: this paper describes our differential FastICA-like algorithms for linear instantaneous and convolutive underdetermined mixture

Integrative machine learning approach for multi-class SCOP protein fold classification

Classification and prediction of protein structure has been a central research theme in structural bioinformatics. Due to the imbalanced distribution of proteins over multi SCOP classification, most discriminative machine learning suffers the well-known ‘False Positives ’ problem when learning over these types of problems. We have devised eKISS, an ensemble machine learning specifically designed to increase the coverage of positive examples when learning under multiclass imbalanced data sets. We have applied eKISS to classify 25 SCOP folds and show that our learning system improved over classical learning methods

Smooth Approximation of Lipschitz functions on Riemannian manifolds

We show that for every Lipschitz function $f$ defined on a separable Riemannian manifold $M$ (possibly of infinite dimension), for every continuous $\epsilon:M\to (0,+\infty)$, and for every positive number $r>0$, there exists a $C^\infty$ smooth Lipschitz function $g:M\to\mathbb{R}$ such that $|f(p)-g(p)|\leq\epsilon(p)$ for every $p\in M$ and $\textrm{Lip}(g)\leq\textrm{Lip}(f)+r$. Consequently, every separable Riemannian manifold is uniformly bumpable. We also present some applications of this result, such as a general version for separable Riemannian manifolds of Deville-Godefroy-Zizler's smooth variational principle.Comment: 10 page

Extended Red Emission and the evolution of carbonaceaous nanograins in NGC 7023

Extended Red Emission (ERE) was recently attributed to the photo-luminescence of either doubly ionized Polycyclic Aromatic Hydrocarbons (PAH$^{++}$), or charged PAH dimers. We analysed the visible and mid-infrared (mid-IR) dust emission in the North-West and South photo-dissociation regions of the reflection nebula NGC 7023.Using a blind signal separation method, we extracted the map of ERE from images obtained with the Hubble Space Telescope, and at the Canada France Hawaii Telescope. We compared the extracted ERE image to the distribution maps of the mid-IR emission of Very Small Grains (VSGs), neutral and ionized PAHs (PAH$^0$ and PAH$^+$) obtained with the Spitzer Space Telescope and the Infrared Space Observatory. ERE is dominant in transition regions where VSGs are being photo-evaporated to form free PAH molecules, and is not observed in regions dominated by PAH$^+$. Its carrier makes a minor contribution to the mid-IR emission spectrum. These results suggest that the ERE carrier is a transition species formed during the destruction of VSGs. Singly ionized PAH dimers appear as good candidates but PAH$^{++}$ molecules seem to be excluded.Comment: Accepted for publication in A&

Large-eddy simulation of the flow in a lid-driven cubical cavity

Large-eddy simulations of the turbulent flow in a lid-driven cubical cavity have been carried out at a Reynolds number of 12000 using spectral element methods. Two distinct subgrid-scales models, namely a dynamic Smagorinsky model and a dynamic mixed model, have been both implemented and used to perform long-lasting simulations required by the relevant time scales of the flow. All filtering levels make use of explicit filters applied in the physical space (on an element-by-element approach) and spectral (modal) spaces. The two subgrid-scales models are validated and compared to available experimental and numerical reference results, showing very good agreement. Specific features of lid-driven cavity flow in the turbulent regime, such as inhomogeneity of turbulence, turbulence production near the downstream corner eddy, small-scales localization and helical properties are investigated and discussed in the large-eddy simulation framework. Time histories of quantities such as the total energy, total turbulent kinetic energy or helicity exhibit different evolutions but only after a relatively long transient period. However, the average values remain extremely close

Mesh update techniques for free-surface flow solvers using spectral element method

This paper presents a novel mesh-update technique for unsteady free-surface Newtonian flows using spectral element method and relying on the arbitrary Lagrangian--Eulerian kinematic description for moving the grid. Selected results showing compatibility of this mesh-update technique with spectral element method are given

Improving Prolog Programs: Refactoring for Prolog

Refactoring is an established technique from the OO-community to restructure code: it aims at improving software readability, maintainability and extensibility. Although refactoring is not tied to the OO-paradigm in particular, its ideas have not been applied to Logic Programming until now. This paper applies the ideas of refactoring to Prolog programs. A catalogue is presented listing refactorings classified according to scope. Some of the refactorings have been adapted from the OO-paradigm, while others have been specifically designed for Prolog. Also the discrepancy between intended and operational semantics in Prolog is addressed by some of the refactorings. In addition, ViPReSS, a semi-automatic refactoring browser, is discussed and the experience with applying \vipress to a large Prolog legacy system is reported. Our main conclusion is that refactoring is not only a viable technique in Prolog but also a rather desirable one.Comment: To appear in ICLP 200

On Distributive Subalgebras of Qualitative Spatial and Temporal Calculi

Qualitative calculi play a central role in representing and reasoning about qualitative spatial and temporal knowledge. This paper studies distributive subalgebras of qualitative calculi, which are subalgebras in which (weak) composition distributives over nonempty intersections. It has been proven for RCC5 and RCC8 that path consistent constraint network over a distributive subalgebra is always minimal and globally consistent (in the sense of strong $n$-consistency) in a qualitative sense. The well-known subclass of convex interval relations provides one such an example of distributive subalgebras. This paper first gives a characterisation of distributive subalgebras, which states that the intersection of a set of $n\geq 3$ relations in the subalgebra is nonempty if and only if the intersection of every two of these relations is nonempty. We further compute and generate all maximal distributive subalgebras for Point Algebra, Interval Algebra, RCC5 and RCC8, Cardinal Relation Algebra, and Rectangle Algebra. Lastly, we establish two nice properties which will play an important role in efficient reasoning with constraint networks involving a large number of variables.Comment: Adding proof of Theorem 2 to appendi