Squaring the Magic

We construct and classify all possible Magic Squares (MS's) related to Euclidean or Lorentzian rank-3 simple Jordan algebras, both on normed division algebras and split composition algebras. Besides the known Freudenthal-Rozenfeld-Tits MS, the single-split G\"unaydin-Sierra-Townsend MS, and the double-split Barton-Sudbery MS, we obtain other 7 Euclidean and 10 Lorentzian novel MS's. We elucidate the role and the meaning of the various non-compact real forms of Lie algebras, entering the MS's as symmetries of theories of Einstein-Maxwell gravity coupled to non-linear sigma models of scalar fields, possibly endowed with local supersymmetry, in D = 3, 4 and 5 space-time dimensions. In particular, such symmetries can be recognized as the U-dualities or the stabilizers of scalar manifolds within space-time with standard Lorentzian signature or with other, more exotic signatures, also relevant to suitable compactifications of the so-called M*- and M'- theories. Symmetries pertaining to some attractor U-orbits of magic supergravities in Lorentzian space-time also arise in this framework.Comment: 21 pages, 1 figure, 20 tables; reference adde

IL-1 regulates the IL-23 response to wheat gliadin, the etiologic agent of Celiac Disease

Celiac disease (CD) is an autoimmune disease prevalent in ~1% of the general population. CD is unique because both the major genetic (Human Leukocyte Antigen-DQ2/DQ8 alleles) and etiologic factors (dietary glutens) for susceptibility are known. While these alleles are responsible for the inappropriate T cell response that characterizes CD, they are not sufficient since most HLA-DQ2+/DQ8+ individuals exposed to glutens never develop disease. The reasons for this have not been explained; however our novel findings strongly advocate a role for interleukin-23 (IL-23) in the immunopathogenesis of CD. We demonstrate that wheat gliadin stimulates monocytes to produce significantly higher amounts of inflammatory cytokines IL-1b, IL-23, and tumor necrosis factor-a (TNFa) in CD patients compared to HLA-DQ2+ healthy individuals. Furthermore, we determine that IL-1 signalling is obligatory for production of IL-23, since IL-1b triggers IL-23 secretion in a dose-dependent manner and IL-1 receptor antagonist (IL-1ra) blocks IL-23 responses to gliadin. Our results suggest that gliadin activation of monocytes and the subsequent robust secretion of IL-1b and IL-23 initiate the immune response cascade that is manifest as CD, and reveal for the first time that the IL-1 system regulates production of IL-23. The discovery of IL-23 has highlighted the critical role of the innate immune response in autoimmunity and other inflammatory conditions. We anticipate that our novel findings will lead to the discovery of therapeutic targets for this disease and other inflammatory diseases mediated by IL-23

Duality, Entropy and ADM Mass in Supergravity

We consider the Bekenstein-Hawking entropy-area formula in four dimensional extended ungauged supergravity and its electric-magnetic duality property. Symmetries of both "large" and "small" extremal black holes are considered, as well as the ADM mass formula for N=4 and N=8 supergravity, preserving different fraction of supersymmetry. The interplay between BPS conditions and duality properties is an important aspect of this investigation.Comment: 45 pages, typos corrected, references adde

S-estimation of hidden Markov models

A method for robust estimation of dynamic mixtures of multivariate distributions is proposed. The EM algorithm is modified by replacing the classical M-step with high breakdown S-estimation of location and scatter, performed by using the bisquare multivariate S-estimator. Estimates are obtained by solving a system of estimating equations that are characterized by component specific sets of weights, based on robust Mahalanobis-type distances. Convergence of the resulting algorithm is proved and its finite sample behavior is investigated by means of a brief simulation study and n application to a multivariate time series of daily returns for seven stock markets

Mothers and fathers with Binge Eating Disorder and their 18-36 months old children: a longitudinal study on parent-infant interactions and offspring\u2019s emotional-behavioral profiles

Maternal Binge Eating Disorder (BED) has been suggested to be associated with poor parent\u2013infant interactions during feeding and with children\u2019s emotional and behavioral problems during infancy (Blissett and Haycraft, 2011). The role of fathers has received increasing consideration in recent years, yet the research has not focused on interactional patterns between fathers with BED and their children. The present study aimed to longitudinally investigate the in\ufb02uence of BED diagnosis, in one or both parents, on parent\u2013infant feeding interactions and on children\u2019s emotional\u2013behavioral functioning. 612 subjects (408 parents; 204 children), recruited in mental health services and pre-schools in Central Italy, were divided into four groups: Group 1 included families with both parents diagnosed with BED, Group 2 and 3 included families with one parent diagnosed with BED, Group 0 was a healthy control. The assessment took place at T1 (18 months of age of children) and T2 (36 months of age of children): feeding interactions were assessed through the Scale for the Assessment of Feeding Interactions (SVIA) while child emotional\u2013behavioral functioning was evaluated with the Child Behavior Check-List (CBCL). When compared to healthy controls, the groups with one or both parents diagnosed with BED showed higher scores on the SVIA and on the CBCL internalizing and externalizing scales, indicating poorer adult\u2013child feeding interactions and higher emotional\u2013behavioral dif\ufb01culties. A direct in\ufb02uence of parental psychiatric diagnosis on the quality of mother\u2013infant and father\u2013infant interactions was also found, both at T1 and T2. Moreover, dyadic feeding interactions mediated the in\ufb02uence of parental diagnosis on children\u2019s psychological functioning. The presence of BED diagnosis in one or both parents seems to in\ufb02uence the severity of maladaptive parent\u2013infant exchanges during feeding and offspring\u2019s emotional\u2013behavioral problems over time, consequently affecting different areas of children\u2019s psychological functioning. This is the \ufb01rst study to demonstrate the speci\ufb01c effects of maternal and paternal BED on infant development. These results could inform prevention and intervention programs in families with one or both parents diagnosed with BED

Multi-Centered Invariants, Plethysm and Grassmannians

Motivated by multi-centered black hole solutions of Maxwell-Einstein theories of (super)gravity in D=4 space-time dimensions, we develop some general methods, that can be used to determine all homogeneous invariant polynomials on the irreducible (SL_h(p,R) x G4)-representation (p,R), where p denotes the number of centers, and SL_h(p,R) is the "horizontal" symmetry of the system, acting upon the indices labelling the centers. The black hole electric and magnetic charges sit in the symplectic representation R of the generalized electric-magnetic (U-)duality group G4. We start with an algebraic approach based on classical invariant theory, using Schur polynomials and the Cauchy formula. Then, we perform a geometric analysis, involving Grassmannians, Pluecker coordinates, and exploiting Bott's Theorem. We focus on non-degenerate groups G4 "of type E7" relevant for (super)gravities whose (vector multiplets') scalar manifold is a symmetric space. In the triality-symmetric stu model of N=2 supergravity, we explicitly construct a basis for the 10 linearly independent degree-12 invariant polynomials of 3-centered black holes.Comment: 1+29 pages, 6 Table

Jordan Frame Supergravity and Inflation in NMSSM

We present a complete explicit N=1, d=4 supergravity action in an arbitrary Jordan frame with non-minimal scalar-curvature coupling of the form $\Phi(z, \bar z)\, R$. The action is derived by suitably gauge-fixing the superconformal action. The theory has a modified Kaehler geometry, and it exhibits a significant dependence on the frame function $\Phi (z, \bar z)$ and its derivatives over scalars, in the bosonic as well as in the fermionic part of the action. Under certain simple conditions, the scalar kinetic terms in the Jordan frame have a canonical form. We consider an embedding of the Next-to-Minimal Supersymmetric Standard Model (NMSSM) gauge theory into supergravity, clarifying the Higgs inflation model recently proposed by Einhorn and Jones. We find that the conditions for canonical kinetic terms are satisfied for the NMSSM scalars in the Jordan frame, which leads to a simple action. However, we find that the gauge singlet field experiences a strong tachyonic instability during inflation in this model. Thus, a modification of the model is required to support the Higgs-type inflation.Comment: 1+36 pages, 4 figures; v2: discussion updated in Subsec. 4.1, Refs. added, typos fixed. To appear in PR

Entanglement, Purity, and Information Entropies in Continuous Variable Systems

Quantum entanglement of pure states of a bipartite system is defined as the amount of local or marginal ({\em i.e.}referring to the subsystems) entropy. For mixed states this identification vanishes, since the global loss of information about the state makes it impossible to distinguish between quantum and classical correlations. Here we show how the joint knowledge of the global and marginal degrees of information of a quantum state, quantified by the purities or in general by information entropies, provides an accurate characterization of its entanglement. In particular, for Gaussian states of continuous variable systems, we classify the entanglement of two--mode states according to their degree of total and partial mixedness, comparing the different roles played by the purity and the generalized $p-$entropies in quantifying the mixedness and bounding the entanglement. We prove the existence of strict upper and lower bounds on the entanglement and the existence of extremally (maximally and minimally) entangled states at fixed global and marginal degrees of information. This results allow for a powerful, operative method to measure mixed-state entanglement without the full tomographic reconstruction of the state. Finally, we briefly discuss the ongoing extension of our analysis to the quantification of multipartite entanglement in highly symmetric Gaussian states of arbitrary $1 \times N$-mode partitions.Comment: 16 pages, 5 low-res figures, OSID style. Presented at the International Conference ``Entanglement, Information and Noise'', Krzyzowa, Poland, June 14--20, 200