The fitting of multifunctions : an approach to nonparametric multimodal regression.

In the last decades a lot of research has been devoted to smoothing in the sense of nonparametric regression. However, this work has nearly exclusively concentrated on fitting regression functions. When the conditional distribution of y|x is multimodal, the assumption of a functional relationship y = m(x) + noise might be too restrictive. We introduce a nonparametric approach to fit multifunctions, allowing to assign a set of output values to a given x. The concept is based on conditional mean shift, which is an easily implemented tool to detect the local maxima of a conditional density function. The methodology is illustrated by environmental data examples

Central Charge Bounds in 4D Conformal Field Theory

We derive model-independent lower bounds on the stress tensor central charge C_T in terms of the operator content of a 4-dimensional Conformal Field Theory. More precisely, C_T is bounded from below by a universal function of the dimensions of the lowest and second-lowest scalars present in the CFT. The method uses the crossing symmetry constraint of the 4-point function, analyzed by means of the conformal block decomposition.Comment: 16 pages, 6 figure

Kinetic energy of a trapped Fermi gas interacting with a Bose-Einstein condensate

We study a confined mixture of bosons and fermions in the regime of quantal degeneracy, with particular attention to the effects of the interactions on the kinetic energy of the fermionic component. We are able to explore a wide region of system parameters by identifying two scaling variables which completely determine its state at low temperature. These are the ratio of the boson-fermion and boson-boson interaction strengths and the ratio of the radii of the two clouds. We find that the effect of the interactions can be sizeable for reasonable choices of the parameters and that its experimental study can be used to infer the sign of the boson-fermion scattering length. The interplay between interactions and thermal effects in the fermionic kinetic energy is also discussed.Comment: REVTEX, 8 pages, 6 figures included. Small corrections to text and figures, accepted for publication in EPJ

Temperature-dependent density profiles of trapped boson-fermion mixtures

We present a semiclassical three-fluid model for a Bose-condensed mixture of interacting Bose and Fermi gases confined in harmonic traps at finite temperature. The model is used to characterize the experimentally relevant behaviour of the equilibrium density profile of the fermions with varying composition and temperature across the onset of degeneracy, for coupling strengths relevant to a mixture of $^{39}$K and $^{40}$K atoms.Comment: 9 pages, 2 postscript figures, accepted for publication in Eur. Phys. Jour.

One-loop adjoint masses for branes at non-supersymmetric angles

This proceeding is based on arXiv:1105.0591 [hep-th] where we consider breaking of supersymmetry in intersecting D-brane configurations by slight deviation of the angles from their supersymmetric values. We compute the masses generated by radiative corrections for the adjoint scalars on the brane world-volumes. In the open string channel, the string two-point function receives contributions only from the infrared limits of N~4 and N~2 supersymmetric configurations, via messengers and their Kaluza-Klein excitations, and leads at leading order to tachyonic directions.Comment: 15 pages, 5 figures. Contribution to the proceedings of the Corfu Summer Institute 2011 School and Workshops on Elementary Particle Physics and Gravity, September 4-18 2011 Corfu, Greec

Factor PD-Clustering

Factorial clustering methods have been developed in recent years thanks to the improving of computational power. These methods perform a linear transformation of data and a clustering on transformed data optimizing a common criterion. Factorial PD-clustering is based on Probabilistic Distance clustering (PD-clustering). PD-clustering is an iterative, distribution free, probabilistic, clustering method. Factor PD-clustering make a linear transformation of original variables into a reduced number of orthogonal ones using a common criterion with PD-Clustering. It is demonstrated that Tucker 3 decomposition allows to obtain this transformation. Factor PD-clustering makes alternatively a Tucker 3 decomposition and a PD-clustering on transformed data until convergence. This method could significantly improve the algorithm performance and allows to work with large dataset, to improve the stability and the robustness of the method

Universal constraints on conformal operator dimensions

We continue the study of model-independent constraints on the unitary conformal field theories (CFTs) in four dimensions, initiated in. Our main result is an improved upper bound on the dimension Δ of the leading scalar operator appearing in the operator product expansion (OPE) of two identical scalars of dimension d: φ d≠1+O δ+.... In the interval 1<1.7 this universal bound takes the form Δ≤2+0.7(d-1)1/2+2. 1(d-1)+0.43(d-1)3/2. The proof is based on prime principles of CFT: unitarity, crossing symmetry, OPE, and conformal block decomposition. We also discuss possible applications to particle phenomenology and, via a 2D analogue, to string theory. © 2009 The American Physical Society

Conformal Field Theories in Fractional Dimensions

We study the conformal bootstrap in fractional space-time dimensions, obtaining rigorous bounds on operator dimensions. Our results show strong evidence that there is a family of unitary CFTs connecting the 2D Ising model, the 3D Ising model, and the free scalar theory in 4D. We give numerical predictions for the leading operator dimensions and central charge in this family at different values of D and compare these to calculations of phi^4 theory in the epsilon-expansion.Comment: 11 pages, 4 figures - references updated - one affiliation modifie

A generalized model of pelagic biogeochemistry for the global ocean ecosystem. Part II: numerical simulations.

This paper presents a global ocean implementation of a multi-component model of marine pelagic biogeochemistry coupled on-line with an ocean general circulation model forced with climatological surface fields (PELAgic biogeochemistry for Global Ocean Simulations, PELAGOS). The final objective is the inclusion of this model as a component in an Earth System model for climate studies. The pelagic model is based on a functional stoichiometric representation of marine biogeochemical cycles and allows simulating the dynamics of C, N, P, Si, O and Fe taking into account the variation of their elemental ratios in the functional groups. The model also includes a parameterization of variable chlorophyll:carbon ratio in phytoplankton, carrying chl as a prognostic variable. The first part of the paper analyzes the contribution of non-local advective-diffusive terms and local vertical processes to the simulated chl distributions. The comparison of the three experiments shows that the mean chl distribution at higher latitudes is largely determined by mixing processes, while vertical advection dominates the distribution in the equatorial upwelling regions. Horizontal advective and diffusive processes are necessary mechanisms for the shape of chl distribution in the sub-tropical Pacific. In the second part, the results have been compared with existing datasets of satellite-derived chlorophyll, surface nutrients, estimates of phytoplankton community composition and primary production data. The agreement is reasonable both in terms of the spatial distribution of annual means and seasonal variability in different dynamical oceanographic regions. Results indicate that some of the model biases in chl and surface nutrients distributions can be related to deficiencies in the simulation of physical processes such as advection and mixing. Other discrepancies are attributed to inadequate parameterizations of phytoplankton functional groups. The model has skill in reproducing the overall distribution of large and small phytoplankton but tends to underestimate diatoms in the northern higher latitudes and overestimate nanophytoplankton with respect to picoautotrophs in oligotrophic regions. The performance of the model is discussed in the context of its use in climate studies and an approach for improving the parameterization of functional groups in deterministic models is outlined

Fermion conformal bootstrap in 4d

We apply numerical conformal bootstrap techniques to the four-point function of a Weyl spinor in 4d non-supersymmetric CFTs. We find universal bounds on operator dimensions and OPE coefficients, including bounds on operators in mixed symmetry representations of the Lorentz group, which were inaccessible in previous bootstrap studies. We find discontinuities in some of the bounds on operator dimensions, and we show that they arise due to a generic yet previously unobserved fake primary effect, which is related to the existence of poles in conformal blocks. We show that this effect is also responsible for similar discontinuities found in four-fermion bootstrap in 3d, as well as in the mixed-correlator analysis of the 3d Ising CFT. As an important byproduct of our work, we develop a practical technology for numerical approximation of general 4d conformal blocks