Zero-variance zero-bias quantum Monte Carlo estimators of the spherically and system-averaged pair density

We construct improved quantum Monte Carlo estimators for the spherically- and system-averaged electron pair density (i.e. the probability density of finding two electrons separated by a relative distance u), also known as the spherically-averaged electron position intracule density I(u), using the general zero-variance zero-bias principle for observables, introduced by Assaraf and Caffarel. The calculation of I(u) is made vastly more efficient by replacing the average of the local delta-function operator by the average of a smooth non-local operator that has several orders of magnitude smaller variance. These new estimators also reduce the systematic error (or bias) of the intracule density due to the approximate trial wave function. Used in combination with the optimization of an increasing number of parameters in trial Jastrow-Slater wave functions, they allow one to obtain well converged correlated intracule densities for atoms and molecules. These ideas can be applied to calculating any pair-correlation function in classical or quantum Monte Carlo calculations.Comment: 13 pages, 9 figures, published versio

Dynamical Symmetry Enlargement Versus Spin-Charge Decoupling in the One-Dimensional SU(4) Hubbard Model

We investigate dynamical symmetry enlargement in the half-filled SU(4) Hubbard chain using non-perturbative renormalization group and Quantum Monte Carlo techniques. A spectral gap is shown to open for arbitrary Coulombic repulsion $U$. At weak coupling, $U \lesssim 3t$, a SO(8) symmetry between charge and spin-orbital excitations is found to be dynamically enlarged at low energy. At strong coupling, $U \gtrsim 6t$, the charge degrees of freedom dynamically decouple and the resulting effective theory in the spin-orbital sector is that of the SO(6) antiferromagnetic Heisenberg model. Both regimes exhibit spin-Peierls order. However, although spin-orbital excitations are $incoherent$ in the SO(6) regime they are $coherent$ in the SO(8) one. The cross-over between these regimes is discussed.Comment: 4 pages, 2 figure

Indigenous children's connectedness to nature: the potential influence of culture, gender and exposure to a contaminated environment

This study investigates the concept of “connectedness to nature” among students from an indigenous Bedouin community, whose relationship with nature is influenced by a variety of cultural, social and environmental factors, not least of which is the fact that the environment in which they live is highly contaminated. We asked 294 fifth- and sixth-grade students (130 boys and 164 girls), who live in the highly rural Bedouin villages in Israel’s Negev desert, to complete an open questionnaire that was specifically designed to elicit detailed information about these particular students’ connection to nature. The paper presents the results of two analyses of this questionnaire. The first—a quantitative analysis—divides the students’ answers into five aspects of connectedness to nature (nature enjoyment, empathy for living creatures, sense of oneness, sense of responsibility and experience of nature in my immediate environment). The second—an inductive, qualitative analysis of the students’ explanations and elaborations of their answers—provides a more nuanced description of the various social, historical and situational factors that influence these students’ relationship with their environment. It then addresses the tension between these two analyses, highlighting the limitations of “traditional” categories of nature connectedness while showing how these can nevertheless be used to elicit detailed, complex and pertinent information. It concludes by demonstrating how this information, if analyzed critically through its correspondence, or lack of correspondence, with the original assumptions of the statements that elicited it, might be used in the development of place-based environmental education programs for specific populations

The Fermion Monte Carlo revisited

In this work we present a detailed study of the Fermion Monte Carlo algorithm (FMC), a recently proposed stochastic method for calculating fermionic ground-state energies [M.H. Kalos and F. Pederiva, Phys. Rev. Lett. vol. 85, 3547 (2000)]. A proof that the FMC method is an exact method is given. In this work the stability of the method is related to the difference between the lowest (bosonic-type) eigenvalue of the FMC diffusion operator and the exact fermi energy. It is shown that within a FMC framework the lowest eigenvalue of the new diffusion operator is no longer the bosonic ground-state eigenvalue as in standard exact Diffusion Monte Carlo (DMC) schemes but a modified value which is strictly greater. Accordingly, FMC can be viewed as an exact DMC method built from a correlated diffusion process having a reduced Bose-Fermi gap. As a consequence, the FMC method is more stable than any transient method (or nodal release-type approaches). We illustrate the various ideas presented in this work with calculations performed on a very simple model having only nine states but a full sign problem. Already for this toy model it is clearly seen that FMC calculations are inherently uncontrolled.Comment: 49 pages with 4 postscript figure

Exact Monte Carlo time dynamics in many-body lattice quantum systems

On the base of a Feynman-Kac--type formula involving Poisson stochastic processes, recently a Monte Carlo algorithm has been introduced, which describes exactly the real- or imaginary-time evolution of many-body lattice quantum systems. We extend this algorithm to the exact simulation of time-dependent correlation functions. The techniques generally employed in Monte Carlo simulations to control fluctuations, namely reconfigurations and importance sampling, are adapted to the present algorithm and their validity is rigorously proved. We complete the analysis by several examples for the hard-core boson Hubbard model and for the Heisenberg model

Mechanisms of cisplatin resistance and targeting of cancer stem cells: Adding glycosylation to the equation

Cisplatin-based chemotherapeutic regimens are the most frequently used (neo)adjuvant treatments for the majority of solid tumors. While platinum-based chemotherapeutic regimens have proven effective against highly proliferative malignant tumors, significant relapse and progression rates as well as decreased overall survival are still observed. Currently, it is known that sub-populations of chemoresistant cells share biological properties with cancer stem cells (CSC), which are believed to be responsible for tumor relapse, invasion and ultimately disease dissemination through acquisition of mesenchymal cell traits. In spite of concentrated efforts devoted to decipher the mechanisms underlying CSC chemoresistance and to design targeted therapeutics to these cells, proteomics has failed to unveil molecular signatures capable of distinguishing between malignant and non-malignant stem cells. This has hampered substantial developments in this complex field. Envisaging a novel rationale for an effective therapy, the current review summarizes the main cellular and molecular mechanisms underlying cisplatin resistance and the impact of chemotherapy challenge in CSC selection and clinical outcome. It further emphasizes the growing amount of data supporting a role for protein glycosylation in drug resistance. The dynamic and context-dependent nature of protein glycosylation is also comprehensively discussed, hence highlighting its potentially important role as a biomarker of CSC. As the paradigm of cancer therapeutics shifts towards precision medicine and patient-tailored therapeutics, we bring into focus the need to introduce glycomics and glycoproteomics in holistic pan-omics models, in order to integrate diverse, multimodal and clinically relevant information towards more effective cancer therapeutics.This work was supported by European Union funds (FEDER/COMPETE) and by national funds (FCT, the Portuguese Foundation for Science and Technology) under the projects with the references FCOMP-01-0124-FEDER 028188 (PTDC/BBB-EBI/0786/2012) and PTDC/BBB-EBI/0567/2014. C.R. acknowledges the support by Gastric Glyco Explorer Initial Training Network (Seventh Framework Programme grant no. 316929). IPATIMUP integrates the i3S Research Unit, which is partially supported by FCT, (PEst-C/SAU/LA0003/2013). Grants were received from FCT: SFRH/BPD/111048/2015 to J.A.F and SFRH/BD/111242/2015 to A.P. FCT is co-financed by European Social Fund (ESF) under Human Potential Operation Programme (POPH) from National Strategic Reference Framework (NSRF)

Zero-variance principle for Monte Carlo algorithms

We present a general approach to greatly increase at little cost the efficiency of Monte Carlo algorithms. To each observable to be computed we associate a renormalized observable (improved estimator) having the same average but a different variance. By writing down the zero-variance condition a fundamental equation determining the optimal choice for the renormalized observable is derived (zero-variance principle for each observable separately). We show, with several examples including classical and quantum Monte Carlo calculations, that the method can be very powerful.Comment: 9 pages, Latex, to appear in Phys. Rev. Let

Insulating charge density wave for a half-filled SU(N) Hubbard model with an attractive on-site interaction in one dimension

We study a one-dimensional SU(N) Hubbard model with an attractive on-site interaction and $N>2$ at half-filling on the bipartite lattice using density-matrix renormalization-group method and a perturbation theory. We find that the ground state of the SU(N) Hubbard model is a charge density wave state with two-fold degeneracy. All the excitations are found to be gapful, resulting in an insulating ground state, on contrary to that in the SU(2) case. Moreover, the charge gap is equal to the Cooperon gap, which behaves as $-2Nt^2/(N-1)U$ in the strong coupling regime. However, the spin gap $\Delta_{s}$ and the quasiparticle gap $\Delta_{1}$ as well open exponentially in the weak coupling region, while in the strong coupling region, they linearly depend on $U$ such that $\Delta_{s}\sim -U(N-1)$ and $\Delta_{1}\sim -U(N-1)/2$.Comment: 7 pages, 7 figure

Equilibrium Sampling From Nonequilibrium Dynamics

We present some applications of an Interacting Particle System (IPS) methodology to the field of Molecular Dynamics. This IPS method allows several simulations of a switched random process to keep closer to equilibrium at each time, thanks to a selection mechanism based on the relative virtual work induced on the system. It is therefore an efficient improvement of usual non-equilibrium simulations, which can be used to compute canonical averages, free energy differences, and typical transitions paths

Effect of Hund coupling in the one-dimensional SU(4) Hubbard model

The one-dimensional SU(4) Hubbard model perturbed by Hund coupling is studied, away from half-filling, by means of renormalization group and bosonization methods. A spectral gap is always present in the spin-orbital sector irrespective of the magnitude of the Coulomb repulsion. We further distinguish between two qualitatively different regimes. At small Hund coupling, we find that the symmetry of the system is dynamically enlarged to SU(4) at low energy with the result of {\it coherent} spin-orbital excitations. When the charge sector is not gapped, a superconducting instability is shown to exist. At large Hund coupling, the symmetry is no longer enlarged to SU(4) and the excitations in the spin sector become {\it incoherent}. Furthermore, the superconductivity can be suppressed in favor of the conventional charge density wave state.Comment: 10 pages, 1 figur