Simulating disordered quantum Ising chains via dense and sparse restricted Boltzmann machines.

In recent years, generative artificial neural networks based on restricted Boltzmann machines (RBMs) have been successfully employed as accurate and flexible variational wave functions for clean quantum many-body systems. In this article, we explore their use in simulations of disordered quantum Ising chains. The standard dense RBM with all-to-all interlayer connectivity is not particularly appropriate for large disordered systems, since in such systems one cannot exploit translational invariance to reduce the amount of parameters to be optimized. To circumvent this problem, we implement sparse RBMs, whereby the visible spins are connected only to a subset of local hidden neurons, thus reducing the amount of parameters. We assess the performance of sparse RBMs as a function of the range of the allowed connections, and we compare it with that of dense RBMs. Benchmark results are provided for two sign-problem-free Hamiltonians, namely pure and random quantum Ising chains. The RBM Ansätzes are trained using the unsupervised learning scheme based on projective quantum Monte Carlo (PQMC) algorithms. We find that the sparse connectivity facilitates the training process and allows sparse RBMs to outperform their dense counterparts. Furthermore, the use of sparse RBMs as guiding functions for PQMC simulations allows us to perform PQMC simulations at a reduced computational cost, avoiding possible biases due to finite random-walker populations. We obtain unbiased predictions for the ground-state energies and the magnetization profiles with fixed boundary conditions, at the ferromagnetic quantum critical point. The magnetization profiles agree with the Fisher-de Gennes scaling relation for conformally invariant systems, including the scaling dimension predicted by the renormalization-group analysis.

Self-learning projective quantum Monte Carlo simulations guided by restricted Boltzmann machines.

The projective quantum Monte Carlo (PQMC) algorithms are among the most powerful computational techniques to simulate the ground-state properties of quantum many-body systems. However, they are efficient only if a sufficiently accurate trial wave function is used to guide the simulation. In the standard approach, this guiding wave function is obtained in a separate simulation that performs a variational minimization. Here we show how to perform PQMC simulations guided by an adaptive wave function based on a restricted Boltzmann machine. This adaptive wave function is optimized along the PQMC simulation via unsupervised machine learning, avoiding the need of a separate variational optimization. As a byproduct, this technique provides an accurate ansatz for the ground-state wave function, which is obtained by minimizing the Kullback-Leibler divergence with respect to the PQMC samples, rather than by minimizing the energy expectation value as in standard variational optimizations. The high accuracy of this self-learning PQMC technique is demonstrated for a paradigmatic sign-problem-free model, namely, the ferromagnetic quantum Ising chain, showing very precise agreement with the predictions of the Jordan-Wigner theory and of loop quantum Monte Carlo simulations performed in the low-temperature limit.

Supervised machine learning of ultracold atoms with speckle disorder.

We analyze how accurately supervised machine learning techniques can predict the lowest energy levels of one-dimensional noninteracting ultracold atoms subject to the correlated disorder due to an optical speckle field. Deep neural networks with different numbers of hidden layers and neurons per layer are trained on large sets of instances of the speckle field, whose energy levels have been preventively determined via a high-order finite difference technique. The Fourier components of the speckle field are used as the feature vector to represent the speckle-field instances. A comprehensive analysis of the details that determine the possible success of supervised machine learning tasks, namely the depth and the width of the neural network, the size of the training set, and the magnitude of the regularization parameter, is presented. It is found that ground state energies of previously unseen instances can be predicted with an essentially negligible error given a computationally feasible number of training instances. First and second excited state energies can be predicted too, albeit with slightly lower accuracy and using more layers of hidden neurons. We also find that a three-layer neural network is remarkably resilient to Gaussian noise added to the training-set data (up to 10% noise level), suggesting that cold-atom quantum simulators could be used to train artificial neural networks.

Quantum Monte Carlo study of a resonant Bose-Fermi mixture.

We study a resonant Bose-Fermi mixture at zero temperature by using the fixed-node diffusion Monte Carlo method. We explore the system from weak to strong boson-fermion interaction, for different concentrations of the bosons relative to the fermion component. We focus on the case where the boson density n(B) is smaller than the fermion density n(F), for which a first-order quantum phase transition is found from a state with condensed bosons immersed in a Fermi sea, to a Fermi-Fermi mixture of composite fermions and unpaired fermions. We obtain the equation of state and the phase diagram, and we find that the region of phase separation shrinks to zero for vanishing n(B).

Repeated inhalation of crack-cocaine affects spermatogenesis in young and adult mice.

To investigate the effects of repeated crack-cocaine inhalation on spermatogenesis of pubertal and mature Balb/c mice, ten young (Y(ex)) and ten adult (A(ex)) Balb/c mice were exposed to the smoke from 5 g of crack with 57.7% of pure cocaine in an inhalation chamber, 5 days/week for 2 months. The young (Y(c)) and adult (A(c)) control animals (n = 10) were kept in a specially built and controlled animal house facility. The morphologic analysis of both testes of all animals included the analysis of quantitative and qualitative histologic parameters to assess the effect of crack-cocaine on spermatogenesis and Leydig cells. Apoptosis was determined by immunolabeling with caspase-3 antibodies. Compared to the Y(c) animals, Y(ex) animals showed a significant reduction in the number of stage VII tubules per testis (p = 0.02), Sertoli cells (p < 0.001) and elongated spermatids (p = 0.001). Comparisons between the Y(ex) and A(ex) groups identified a significant reduction in the number of Sertoli cells (p < 0.001) and round spermatids (p < 0.001) in the Y(ex) group and a significant increase in apoptotic Leydig cells (p = 0.04) in the A(ex) group. The experimental results indicate that crack-cocaine smoke inhalation induced spermatogenesis disruption in chronically exposed mice, particularly in pubertal mice.

Density and spin response of a strongly interacting Fermi gas in the attractive and quasirepulsive regime.

Recent experimental advances in ultracold Fermi gases allow for exploring response functions under different dynamical conditions. In particular, the issue of obtaining a "quasirepulsive" regime starting from a Fermi gas with an attractive interparticle interaction while avoiding the formation of the two-body bound state is currently debated. Here, we provide a calculation of the density and spin response for a wide range of temperature and coupling both in the attractive and quasirepulsive regime, whereby the system is assumed to evolve nonadiabatically toward the "upper branch" of the Fermi gas. A comparison is made with the available experimental data for these two quantities.

Evolution of the normal state of a strongly interacting Fermi gas from a pseudogap phase to a molecular Bose gas.

Wave-vector resolved radio frequency spectroscopy data for an ultracold trapped Fermi gas are reported for several couplings at T(c), and extensively analyzed in terms of a pairing-fluctuation theory. We map the evolution of a strongly interacting Fermi gas from the pseudogap phase into a fully gapped molecular Bose gas as a function of the interaction strength, which is marked by a rapid disappearance of a remnant Fermi surface in the single-particle dispersion. We also show that our theory of a pseudogap phase is consistent with a recent experimental observation as well as with quantum Monte Carlo data of thermodynamic quantities of a unitary Fermi gas above T(c).

Penile anthropometry in systemic lupus erythematosus patients.

The aim of this study was to evaluate penile anthropometry in systemic lupus erythematosus (SLE) patients compared with healthy controls and the possible relevant pubertal, clinical, hormonal and treatment factors that could influence penile dimensions. Twenty-five consecutive SLE patients were assessed by urological examination, sexual function, testicular ultrasound, hormones, sperm analysis, genetic analysis, clinical features and treatment. The control group included 25 age-matched healthy males. SLE patients had a lower median penis length and circumference [8 (7.5-10) vs. 10 (8-13) cm, p = 0.0001; 8 (7-10) vs. 10 (7-11) cm, p = 0.001; respectively], lower median testicular volume by right and left Prader [15 (10-25) vs. 20 (12-25) ml, p = 0.003; 15 (10-25) vs. 20 (12-25) ml, p = 0.006; respectively], higher median of follicle-stimulating hormone [5.8 (2.1-25) vs. 3.3 (1.9-9) IU/l, p = 0.002] and lower morning total testosterone levels (28% vs. 0%, p = 0.009) compared with controls. In spite of that, erectile dysfunction was not observed in patients or controls. Analyses of lupus patients revealed that the median penis circumference was lower in patients with disease onset before first ejaculation compared with those with disease onset after first ejaculation [7.8 (7-10) vs. 9.0 (7.5-10) cm, p = 0.026]. No differences were observed in the median penile anthropometry regarding sexual dysfunction (p = 0.610), lower morning total testosterone levels (p = 0.662), oligo/azoospermia (p = 0.705), SLE Disease Activity Index ≥ 4 (p = 0.562), Systemic Lupus International Collaborating Clinics/ACR Damage Index ≥ 1 (p = 0.478), prednisone cumulative dose (p = 0.789) and intravenous cyclophosphamide therapy (p = 0.754). Klinefelters syndrome (46XY/47XXY) was diagnosed in one (4%) SLE patient with decreased penile size whereas Y-chromosomal microdeletions was absent in all of them. In conclusion, we have identified reduced penile dimensions in SLE patients with no deleterious effect in erectile function. Disease onset before first ejaculation seems to affect penis development in pre-pubertal lupus.

Competition between final-state and pairing-gap effects in the radio-frequency spectra of ultracold Fermi atoms.

The radio-frequency spectra of ultracold Fermi atoms are calculated by including final-state interactions affecting the excited level of the transition and compared with the experimental data. A competition is revealed between pairing-gap effects which tend to push the oscillator strength toward high frequencies away from threshold and final-state effects which tend instead to pull the oscillator strength toward threshold. As a result of this competition, the position of the peak of the spectra cannot be simply related to the value of the pairing gap, whose extraction thus requires support from theoretical calculations.

Josephson effect throughout the BCS-BEC crossover.

We study the stationary Josephson effect for neutral fermions across the BCS-BEC (Bose-Einstein condensate) crossover, by solving numerically the Bogoliubov-de Gennes equations at zero temperature. The Josephson current is found to be considerably enhanced for all barriers at about unitarity. For vanishing barrier, the Josephson critical current approaches the Landau limiting value which, depending on the coupling, is determined by either pair-breaking or sound-mode excitations. In the coupling range from the BCS limit to unitarity, a procedure is proposed to extract the pairing gap from the Landau limiting current.

Biochemical and bioimaging markers for risk assessment and diagnosis in major cardiovascular diseases: a road to integration of complementary diagnostic tools.

This report from the first International Course on Integrated Biomarkers, Biochemical and Bioimaging Endpoints in Cardiovascular Diagnosis, Prevention, Therapy and Drug Development provides the basis for optimizing diagnostic, prognostic and therapeutic information in four areas of cardiovascular medicine: primary prevention of cardiovascular diseases, acute coronary syndromes, heart failure and stroke. Risk stratification and treatment strategies can be refined and enhanced through integration of bioimaging and biochemical markers to characterize sub-clinical and clinical atherosclerosis. For the integrative approach to be useful, each of the biomarkers must be validated and cost-effective. Clinical decision is the primary level of integration and is based on clinical evaluation and the use of a combination of bioimaging and biochemical markers. The decision to initiate preventive or therapeutic intervention must take into account the factors affecting the levels of expression of the biomarker and the potential input the biomarker has on metabolic processes or modulation of other biomarkers. The optimal approach to intervention must take into consideration the risk-benefit and cost-effectiveness ratios.

Microclimate influence on mineral and metabolic profiles of grape berries.

The grape berry microclimate is known to influence berry quality. The effects of the light exposure of grape berry clusters on the composition of berry tissues were studied on the "Merlot" variety grown in a vineyard in Bordeaux, France. The light exposure of the fruiting zone was modified using different intensities of leaf removal, cluster position relative to azimuth, and berry position in the cluster. Light exposures were identified and classified by in situ measurements of berry temperatures. Berries were sampled at maturity (>19 Brix) for determination of skin and/or pulp chemical and metabolic profiles based on (1) chemical and physicochemical measurement of minerals (N, P, K, Ca, Mg), (2) untargeted 1H NMR metabolic fingerprints, and HPLC targeted analyses of (3) amino acids and (4) phenolics. Each profile defined by partial least-square discriminant analysis allowed us to discriminate berries from different light exposure. Discriminant compounds between shaded and light-exposed berries were quercetin-3-glucoside, kaempferol-3-glucoside, myricetin-3-glucoside, and isorhamnetin-3-glucoside for the phenolics, histidine, valine, GABA, alanine, and arginine for the amino acids, and malate for the organic acids. Capacities of the different profiling techniques to discriminate berries were compared. Although the proportion of explained variance from the 1H NMR fingerprint was lower compared to that of chemical measurements, NMR spectroscopy allowed us to identify lit and shaded berries. Light exposure of berries increased the skin and pulp flavonols, histidine and valine contents, and reduced the organic acids, GABA, and alanine contents. All the targeted and nontargeted analytical data sets used made it possible to discriminate sun-exposed and shaded berries. The skin phenolics pattern was the most discriminating and allowed us to sort sun from shade berries. These metabolite classes can be used to qualify berries collected in an undetermined environment. The physiological significance of light and temperature effects on berry composition is discussed.

Trapped fermions with density imbalance in the Bose-Einstein condensate limit.

We analyze the effects of imbalancing the populations of two-component trapped fermions, in the Bose-Einstein condensate limit of the attractive interaction between different fermions. Starting from the gap equation with two fermionic chemical potentials, we derive a set of coupled equations that describe composite bosons and excess fermions. We include in these equations the processes leading to the correct dimer-dimer and dimer-fermion scattering lengths. The coupled equations are then solved in the Thomas-Fermi approximation to obtain the density profiles for composite bosons and excess fermions, which are relevant to the recent experiments with trapped fermionic atoms.

Extracting the condensate density from projection experiments with Fermi gases.

A debated issue in the physics of the BCS-BEC crossover with trapped Fermi atoms is to identify characteristic properties of the superfluid phase. Recently, a condensate fraction was measured on the BCS side of the crossover by sweeping the system in a fast (nonadiabatic) way from the BCS to the Bose-Einstein condensation (BEC) sides, thus "projecting" the initial many-body state onto a molecular condensate. We analyze here the theoretical implications of these projection experiments, by identifying the appropriate quantum-mechanical operator associated with the measured quantities and relating them to the many-body correlations occurring in the BCS-BEC crossover. Calculations are presented over wide temperature and coupling ranges, by including pairing fluctuations on top of the mean field.

Quantitative comparison between theoretical predictions and experimental results for the BCS-BEC crossover.

Theoretical predictions for the Bardeen-Cooper-Schrieffer-Bose-Einstein condensation crossover of trapped Fermi atoms are compared with recent experimental results for the density profiles of 6Li. The calculations rest on a single theoretical approach that includes pairing fluctuations beyond mean-field. Excellent agreement with experimental results is obtained. Theoretical predictions for the zero-temperature chemical potential and gap at the unitarity limit are also found to compare extremely well with Quantum Monte Carlo simulations and with recent experimental results.

BCS-BEC crossover at finite temperature for superfluid trapped Fermi atoms.

We consider the BCS-BEC (Bose-Einstein-condensate) crossover for a system of trapped Fermi atoms at finite temperature, both below and above the superfluid critical temperature, by including fluctuations beyond mean field. We determine the superfluid critical temperature and the pair-breaking temperature as functions of the attractive interaction between Fermi atoms, from the weak- to the strong-coupling limit (where bosonic molecules form as bound-fermion pairs). Density profiles in the trap are also obtained for all temperatures and couplings.

Pairing fluctuation effects on the single-particle spectra for the superconducting state.

Single-particle spectra are calculated in the superconducting state for a fermionic system with an attractive interaction, as functions of temperature and coupling strength from weak to strong. The fermionic system is described by a single-particle self-energy that includes pairing-fluctuation effects in the superconducting state. The theory reduces to the ordinary BCS approximation in weak coupling and to the Bogoliubov approximation for the composite bosons in strong coupling. Several features of the single-particle spectral function are shown to compare favorably with experimental data for cuprate superconductors.

Derivation of the Gross-Pitaevskii equation for condensed bosons from the Bogoliubov-de Gennes equations for superfluid fermions.

We derive the time-independent Gross-Pitaevskii equation at zero temperature for condensed bosons, which form as bound-fermion pairs when the mutual fermionic attractive interaction is sufficiently strong, from the strong-coupling limit of the Bogoliubov-de Gennes equations that describe superfluid fermions in the presence of an external potential. Three-body corrections to the Gross-Pitaevskii equation are also obtained by our approach. Our results are relevant to the recent advances with ultracold fermionic atoms in a trap.

Magnetic field effect on the pseudogap temperature within precursor superconductivity.

We determine the magnetic-field dependence of the pseudogap closing temperature T* within a precursor superconductivity scenario. Detailed calculations with an anisotropic lattice model with d-wave superconductivity account for a recently determined experimental relation in BSCCO between the pseudogap closing field and the pseudogap temperature at zero field, as well as for the weak initial dependence of T* at low fields. Our results indicate that the available experimental data are fully compatible with a superconducting origin of the pseudogap in cuprate superconductors.