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Developmental Dyslexia (DD) is a learning disability related to the acquisition of reading skills that affects about 5% of the population. DD can have an enormous impact on the intellectual and personal development of affected children, so early detection is key to implementing preventive strategies for teaching language. Research has shown that there may be biological underpinnings to DD that affect phoneme processing, and hence these symptoms may be identifiable before reading ability is acquired, allowing for early intervention. In this paper we propose a new methodology to assess the risk of DD before students learn to read. For this purpose, we propose a mixed neural model that calculates risk levels of dyslexia from tests that can be completed at the age of 5 years. Our method first trains an auto-encoder, and then combines the trained encoder with an optimized ordinal regression neural network devised to ensure consistency of predictions. Our experiments show that the system is able to detect unaffected subjects two years before it can assess the risk of DD based mainly on phonological processing, giving a specificity of 0.969 and a correct rate of more than 0.92. In addition, the trained encoder can be used to transform test results into an interpretable subject spatial distribution that facilitates risk assessment and validates methodology., Comment: 12 pages, 4 figures

From the diversity of applications of Network Science, in this Opinion Paper we are concerned about its potential to analyze one of the most extended group sports: Football (soccer in U.S. terminology). As we will see, Network Science allows addressing different aspects of the team organization and performance not captured by classical analyses based on the performance of individual players. The reason behind relies on the complex nature of the game, which, paraphrasing the foundational paradigm of complexity sciences "can not be analyzed by looking at its components (i.e., players) individually but, on the contrary, considering the system as a whole" or, in the classical words of after-match interviews "it's not just me, it's the team"., Comment: 7 pages, 1 figure

This paper defines and investigates nonsymmetric Macdonald polynomials with values in an irreducible module of the Hecke algebra of type $A_{N-1}$. These polynomials appear as simultaneous eigenfunctions of Cherednik operators. Several objects and properties are analyzed, such as the canonical bilinear form which pairs polynomials with those arising from reciprocals of the original parameters, and the symmetrization of the Macdonald polynomials. The main tool of the study is the Yang-Baxter graph. We show that these Macdonald polynomials can be easily computed following this graph. We give also an interpretation of the symmetrization and the bilinear forms applied to the Macdonald polynomials in terms of the Yang-Baxter graph., Comment: 85 pages, 5 figures

Fractional quantum Hall states of particles in the lowest Landau levels are described by multivariate polynomials. The incompressible liquid states when described on a sphere are fully invariant under the rotation group. Excited quasiparticle/quasihole states are member of multiplets under the rotation group and generically there is a nontrivial highest weight member of the multiplet from which all states can be constructed. Some of the trial states proposed in the literature belong to classical families of symmetric polynomials. In this paper we study Macdonald and Jack polynomials that are highest weight states. For Macdonald polynomials it is a (q,t)-deformation of the raising angular momentum operator that defines the highest weight condition. By specialization of the parameters we obtain a classification of the highest weight Jack polynomials. Our results are valid in the case of staircase and rectangular partition indexing the polynomials., Comment: 17 pages, published version

A new model for elucidating the mathematical foundation of plasticity yield criteria is proposed. The proposed ansatz uses differential geometry and group theory concepts in addition to elementary hypotheses based on well-established experimental evidence. Its theoretical development involves the analysis of tensor functions and provides a series expansion which allows the functional stress-dependence of plasticity yield criteria to be predicted. The theoretical framework for the model includes a series of spatial coefficients that provide a more flexible theory for in-depth examination of symmetry and anisotropy in compact solid materials. It describes the classical yield criteria (like those of Tresca, Von Mises, Hosford, Hill, etc) and accurately describes the anomalous behaviour of metals such as aluminium, which was elucidated by Hill (1979). Further, absolutely new instances of stress-dependence are predicted; this makes it highly useful for fitting experimental data with a view to studying the phenomena behind plasticity., Comment: 31 pages, 5 figures

We extend to several combinatorial Hopf algebras the endomorphism of symmetric functions sending the first power-sum to zero and leaving the other ones invariant. As a transformation of alphabets, this is the (1-E)-transform, where E is the exponential alphabet, whose elementary symmetric functions are e_n=1/n!. In the case of noncommutative symmetric functions, we recover Schocker's idempotents for derangement numbers [Discr. Math. 269 (2003), 239]. From these idempotents, we construct subalgebras of the descent algebras analogous to the peak algebras and study their representation theory. The case of WQSym leads to similar subalgebras of the Solomon-Tits algebras. In FQSym, the study of the transformation boils down to a simple solution of the Tsetlin library in the uniform case., Comment: 33 pages

We study the invariant theory of trilinear forms over a three-dimensional complex vector space, and apply it to investigate the behaviour of pure entangled three-partite qutrit states and their normal forms under local filtering operations (SLOCC). We describe the orbit space of the SLOCC group $SL(3,\C)^{\times 3}$ both in its affine and projective versions in terms of a very symmetric normal form parameterized by three complex numbers. The parameters of the possible normal forms of a given state are roots of an algebraic equation, which is proved to be solvable by radicals. The structure of the sets of equivalent normal forms is related to the geometry of certain regular complex polytopes., Comment: 19 pages, revtex4, three figures; revised version

We obtain a complete and minimal set of 170 generators for the algebra of $SL(2,\C)^{\times 4}$-covariants of a binary quadrilinear form. Interpreted in terms of a four qubit system, this describes in particular the algebraic varieties formed by the orbits of local filtering operations in its projective Hilbert space. Also, this sheds some light on the local unitary invariants, and provides all the possible building blocks for the construction of entanglement measures for such a system., Comment: 14 pages, IOP macros; slightly expanded version

We describe explicitly the algebra of polynomial functions on the Hilbert space of four qubit states which are invariant under the SLOCC group $SL(2,{\mathbb C})^{4}$. From this description, we obtain a closed formula for the hyperdeterminant in terms of low degree invariants., Comment: 5 pages, revtex4; some typos corrected

We investigate the simplest class of hyperdeterminants defined by Cayley in the case of Hankel hypermatrices (tensors of the form $A_{i_1i_2... i_k}=f(i_1+i_2+...+i_k)$). It is found that many classical properties of Hankel determinants can be generalized, and a connection with Selberg type integrals is established. In particular, Selberg's original formula amounts to the evaluation of all Hankel hyperdeterminants built from the moments of the Jacobi polynomials. Many higher-dimensional analogues of classical Hankel determinants are evaluated in closed form. The Toeplitz case is also briefly discussed. In physical terms, both cases are related to the partition functions of one-dimensional Coulomb systems with logarithmic potential., Comment: 32 pages, LaTex, IOP macros

Chen's lemma on iterated integrals implies that certain identities involving multiple integrals, such as the de Bruijn and Wick formulas, amount to combinatorial identities for Pfaffians and hafnians in shuffle algebras. We provide direct algebraic proofs of such shuffle identities, and obtain various generalizations. We also discuss some Pfaffian identities due to Sundquist and Ishikawa-Wakayama, and a Cauchy formula for anticommutative symmetric functions. Finally, we extend some of the previous considerations to hyperpfaffians and hyperhafnians., Comment: 28 pages, LaTex. Minor typos corrected, two references added