ClassTAL

This is the description of a Matlab script (classTAL.m) that automatically classifies BrainVoyager .voi maps with afni brain atlas. The script saves many useful output files

The Pad\'e iterations for the matrix sign function and their reciprocals are optimal

It is proved that among the rational iterations locally converging with order s>1 to the sign function, the Pad\'e iterations and their reciprocals are the unique rationals with the lowest sum of the degrees of numerator and denominator

Multimodal music information processing and retrieval: survey and future challenges

Towards improving the performance in various music information processing tasks, recent studies exploit different modalities able to capture diverse aspects of music. Such modalities include audio recordings, symbolic music scores, mid-level representations, motion, and gestural data, video recordings, editorial or cultural tags, lyrics and album cover arts. This paper critically reviews the various approaches adopted in Music Information Processing and Retrieval and highlights how multimodal algorithms can help Music Computing applications. First, we categorize the related literature based on the application they address. Subsequently, we analyze existing information fusion approaches, and we conclude with the set of challenges that Music Information Retrieval and Sound and Music Computing research communities should focus in the next years

The topology of the external activity complex of a matroid

We prove that the external activity complex $\textrm{Act}_<(M)$ of a matroid is shellable. In fact, we show that every linear extension of LasVergnas's external/internal order $<_{ext/int}$ on $M$ provides a shelling of $\textrm{Act}_<(M)$. We also show that every linear extension of LasVergnas's internal order $<_{int}$ on $M$ provides a shelling of the independence complex $IN(M)$. As a corollary, $\textrm{Act}_<(M)$ and $M$ have the same $h$-vector. We prove that, after removing its cone points, the external activity complex is contractible if $M$ contains $U_{3,1}$ as a minor, and a sphere otherwise.Comment: Comments are welcom

Coxeter submodular functions and deformations of Coxeter permutahedra

We describe the cone of deformations of a Coxeter permutahedron, or equivalently, the nef cone of the toric variety associated to a Coxeter complex. This family of polytopes contains polyhedral models for the Coxeter-theoretic analogs of compositions, graphs, matroids, posets, and associahedra. Our description extends the known correspondence between generalized permutahedra, polymatroids, and submodular functions to any finite reflection group.Comment: Minor edits. To appear in Advances of Mathematic

Torsion zero cycles with modulus on affine varieties

In this note we show that given a smooth affine variety $X$ over an algebraically closed field $k$ and an effective (possibly non reduced) Cartier divisor $D$ on it, the Kerz-Saito Chow group of zero cycles with modulus ${\rm CH}_0(X|D)$ is torsion free, except possibly for $p$-torsion if the characteristic of $k$ is $p>0$. This generalizes to the relative setting classical theorems of Rojtman (for $X$ smooth) and of Levine (for $X$ singular). A stronger version of this result, that encompasses $p$-torsion as well, was proven with a different and more sophisticated method by A. Krishna and the author in another paper.Comment: Final version. 12 pages, exposition improved. Several gaps in the proofs fixe