Multi-task Regression using Minimal Penalties

In this paper we study the kernel multiple ridge regression framework, which we refer to as multi-task regression, using penalization techniques. The theoretical analysis of this problem shows that the key element appearing for an optimal calibration is the covariance matrix of the noise between the different tasks. We present a new algorithm to estimate this covariance matrix, based on the concept of minimal penalty, which was previously used in the single-task regression framework to estimate the variance of the noise. We show, in a non-asymptotic setting and under mild assumptions on the target function, that this estimator converges towards the covariance matrix. Then plugging this estimator into the corresponding ideal penalty leads to an oracle inequality. We illustrate the behavior of our algorithm on synthetic examples

Improving prediction performance of stellar parameters using functional models

This paper investigates the problem of prediction of stellar parameters, based on the star's electromagnetic spectrum. The knowledge of these parameters permits to infer on the evolutionary state of the star. From a statistical point of view, the spectra of different stars can be represented as functional data. Therefore, a two-step procedure decomposing the spectra in a functional basis combined with a regression method of prediction is proposed. We also use a bootstrap methodology to build prediction intervals for the stellar parameters. A practical application is also provided to illustrate the numerical performance of our approach

Engineering SU(2) invariant spin models to mimic quantum dimer physics on the square lattice

We consider the spin-1/2 hamiltonians proposed by Cano and Fendley [J. Cano and P. Fendley, Phys. Rev. Lett. 105, 067205 (2010)] which were built to promote the well-known Rokshar-Kivelson (RK) point of quantum dimer models to spin-1/2 wavefunctions. We first show that these models, besides the exact degeneracy of RK point, support gapless spinless excitations as well as a spin gap in the thermodynamic limit, signatures of an unusual spin liquid. We then extend the original construction to create a continuous family of SU(2) invariant spin models that reproduces the phase diagram of the quantum dimer model, and in particular show explicit evidences for existence of columnar and staggered phases. The original models thus appear as multicritical points in an extended phase diagram. Our results are based on the use of a combination of numerical exact simulations and analytical mapping to effective generalized quantum dimer models.Comment: 12 pages, 8 figure

Learning the distribution of latent variables in paired comparison models with round-robin scheduling

Paired comparison data considered in this paper originate from the comparison of a large number N of individuals in couples. The dataset is a collection of results of contests between two individuals when each of them has faced n opponents, where n is much larger than N. Individual are represented by independent and identically distributed random parameters characterizing their abilities.The paper studies the maximum likelihood estimator of the parameters distribution. The analysis relies on the construction of a graphical model encoding conditional dependencies of the observations which are the outcomes of the first n contests each individual is involved in. This graphical model allows to prove geometric loss of memory properties and deduce the asymptotic behavior of the likelihood function. This paper sets the focus on graphical models obtained from round-robin scheduling of these contests.Following a classical construction in learning theory, the asymptotic likelihood is used to measure performance of the maximum likelihood estimator. Risk bounds for this estimator are finally obtained by sub-Gaussian deviation results for Markov chains applied to the graphical model

Entanglement of quantum spin systems: a valence-bond approach

In order to quantify entanglement between two parts of a quantum system, one of the most used estimator is the Von Neumann entropy. Unfortunately, computing this quantity for large interacting quantum spin systems remains an open issue. Faced with this difficulty, other estimators have been proposed to measure entanglement efficiently, mostly by using simulations in the valence-bond basis. We review the different proposals and try to clarify the connections between their geometric definitions and proper observables. We illustrate this analysis with new results of entanglement properties of spin 1 chains.Comment: Proceedings of StatPhys 24 satellite conference in Hanoi; submitted for a special issue of Modern Physics Letters

Valence bond entanglement entropy of frustrated spin chains

We extend the definition of the recently introduced valence bond entanglement entropy to arbitrary SU(2) wave functions of S=1/2 spin systems. Thanks to a reformulation of this entanglement measure in terms of a projection, we are able to compute it with various numerical techniques for frustrated spin models. We provide extensive numerical data for the one-dimensional J1-J2 spin chain where we are able to locate the quantum phase transition by using the scaling of this entropy with the block size. We also systematically compare with the scaling of the von Neumann entanglement entropy. We finally underline that the valence-bond entropy definition does depend on the choice of bipartition so that, for frustrated models, a "good" bipartition should be chosen, for instance according to the Marshall sign.Comment: 10 pages, 6 figures; v2: published versio

Numerical Contractor Renormalization Method for Quantum Spin Models

We demonstrate the utility of the numerical Contractor Renormalization (CORE) method for quantum spin systems by studying one and two dimensional model cases. Our approach consists of two steps: (i) building an effective Hamiltonian with longer ranged interactions using the CORE algorithm and (ii) solving this new model numerically on finite clusters by exact diagonalization. This approach, giving complementary information to analytical treatments of the CORE Hamiltonian, can be used as a semi-quantitative numerical method. For ladder type geometries, we explicitely check the accuracy of the effective models by increasing the range of the effective interactions. In two dimensions we consider the plaquette lattice and the kagome lattice as non-trivial test cases for the numerical CORE method. On the plaquette lattice we have an excellent description of the system in both the disordered and the ordered phases, thereby showing that the CORE method is able to resolve quantum phase transitions. On the kagome lattice we find that the previously proposed twofold degenerate S=1/2 basis can account for a large number of phenomena of the spin 1/2 kagome system. For spin 3/2 however this basis does not seem to be sufficient anymore. In general we are able to simulate system sizes which correspond to an 8x8 lattice for the plaquette lattice or a 48-site kagome lattice, which are beyond the possibilities of a standard exact diagonalization approach.Comment: 15 page

Towards the total synthesis of lactonamycin

The natural product lactonamycin (1) was isolated in Japan by Matsomoto et al.. Biological evaluation of lactonamycin (1) against Gram-positive bacteria such as Staphylococcus aureus showed significant levels of antimicrobial activity and it was especially active against clinically isolated-MRSA and - VRE. In addition to interesting biological properties, lactonamycin (1) possesses an intriguing molecular architecture (Figure 1). The novel, highly functionalized hexacyclic aglycone core, known as lactonamycinone (2) contains, in the western half, a highly-oxygenated fused perhydrofuranfuranone bicycle connected to a labile tertiary methoxy group, and in the eastern half, a naphtha[e]isoindole ring system. Adding to the structural complexity of lactonamycin (1), a 2,3,6- trideoxy sugar unit is connected to the core via a highly hindered tertiary glycosidic linkage. [Molecular structure diagrams appear here. To view, please open pdf attachment] Figure 1 - Structures of lactonamycin (1) and lactonamycinone (2). A key step in the current strategy is an electrodecarboxylation reaction to introduce the angular methoxy group. Various experiments towards this electrodecarboxylation reaction are described using simple model substrates. In particular, the synthesis of model system (3) and investigations towards ABCD tetracycle model system (4) are described alongside our efforts towards the synthesis of lactonamycin (1) (Figure 2). Finally, a new synthesis of known boronic ester 5 was investigated using the biomimetic resorcylate methodology developed in the group. [Molecular structure diagrams appear here. To view, please open pdf attachment] Figure 2 – Structures of carboxylic model system 3, ABCD tetracycle model system 4 and boronic ester 5

Microwave-stimulated Raman adiabatic passage in a Bose-Einstein condensate on an atom chip

We report the achievement of stimulated Raman adiabatic passage (STIRAP) in the microwave frequency range between internal states of a Bose-Einstein condensate (BEC) magnetically trapped in the vicinity of an atom chip. The STIRAP protocol used in this experiment is robust to external perturbations as it is an adiabatic transfer, and power-efficient as it involves only resonant (or quasi-resonant) processes. Taking into account the effect of losses and collisions in a non-linear Bloch equations model, we show that the maximum transfer efficiency is obtained for non-zero values of the one- and two-photon detunings, which is confirmed quantitatively by our experimental measurements