Recent Developments of World-Line Monte Carlo Methods

World-line quantum Monte Carlo methods are reviewed with an emphasis on breakthroughs made in recent years. In particular, three algorithms -- the loop algorithm, the worm algorithm, and the directed-loop algorithm -- for updating world-line configurations are presented in a unified perspective. Detailed descriptions of the algorithms in specific cases are also given.Comment: To appear in Journal of Physical Society of Japa

Schwinger-Dyson equations in large-N quantum field theories and nonlinear random processes

We propose a stochastic method for solving Schwinger-Dyson equations in large-N quantum field theories. Expectation values of single-trace operators are sampled by stationary probability distributions of the so-called nonlinear random processes. The set of all histories of such processes corresponds to the set of all planar diagrams in the perturbative expansions of the expectation values of singlet operators. We illustrate the method on the examples of the matrix-valued scalar field theory and the Weingarten model of random planar surfaces on the lattice. For theories with compact field variables, such as sigma-models or non-Abelian lattice gauge theories, the method does not converge in the physically most interesting weak-coupling limit. In this case one can absorb the divergences into a self-consistent redefinition of expansion parameters. Stochastic solution of the self-consistency conditions can be implemented as a "memory" of the random process, so that some parameters of the process are estimated from its previous history. We illustrate this idea on the example of two-dimensional O(N) sigma-model. Extension to non-Abelian lattice gauge theories is discussed.Comment: 16 pages RevTeX, 14 figures; v2: Algorithm for the Weingarten model corrected; v3: published versio

Fidelity susceptibility made simple: A unified quantum Monte Carlo approach

The fidelity susceptibility is a general purpose probe of phase transitions. With its origin in quantum information and in the differential geometry perspective of quantum states, the fidelity susceptibility can indicate the presence of a phase transition without prior knowledge of the local order parameter, as well as reveal the universal properties of a critical point. The wide applicability of the fidelity susceptibility to quantum many-body systems is, however, hindered by the limited computational tools to evaluate it. We present a generic, efficient, and elegant approach to compute the fidelity susceptibility of correlated fermions, bosons, and quantum spin systems in a broad range of quantum Monte Carlo methods. It can be applied both to the ground-state and non-zero temperature cases. The Monte Carlo estimator has a simple yet universal form, which can be efficiently evaluated in simulations. We demonstrate the power of this approach with applications to the Bose-Hubbard model, the spin-$1/2$ XXZ model, and use it to examine the hypothetical intermediate spin-liquid phase in the Hubbard model on the honeycomb lattice.Comment: new physical insight added in Sec. VI., improved data in Fig.

Modeling the ballistic-to-diffusive transition in nematode motility reveals variation in exploratory behavior across species

A quantitative understanding of organism-level behavior requires predictive models that can capture the richness of behavioral phenotypes, yet are simple enough to connect with underlying mechanistic processes. Here we investigate the motile behavior of nematodes at the level of their translational motion on surfaces driven by undulatory propulsion. We broadly sample the nematode behavioral repertoire by measuring motile trajectories of the canonical lab strain $C. elegans$ N2 as well as wild strains and distant species. We focus on trajectory dynamics over timescales spanning the transition from ballistic (straight) to diffusive (random) movement and find that salient features of the motility statistics are captured by a random walk model with independent dynamics in the speed, bearing and reversal events. We show that the model parameters vary among species in a correlated, low-dimensional manner suggestive of a common mode of behavioral control and a trade-off between exploration and exploitation. The distribution of phenotypes along this primary mode of variation reveals that not only the mean but also the variance varies considerably across strains, suggesting that these nematode lineages employ contrasting ``bet-hedging'' strategies for foraging.Comment: 46 pages, 18 figures, 6 table

Genome-wide analysis of ivermectin response by Onchocerca volvulus reveals that genetic drift and soft selective sweeps contribute to loss of drug sensitivity

Treatment of onchocerciasis using mass ivermectin administration has reduced morbidity and transmission throughout Africa and Central/South America. Mass drug administration is likely to exert selection pressure on parasites, and phenotypic and genetic changes in several Onchocerca volvulus populations from Cameroon and Ghana-exposed to more than a decade of regular ivermectin treatment-have raised concern that sub-optimal responses to ivermectin's anti-fecundity effect are becoming more frequent and may spread.Pooled next generation sequencing (Pool-seq) was used to characterise genetic diversity within and between 108 adult female worms differing in ivermectin treatment history and response. Genome-wide analyses revealed genetic variation that significantly differentiated good responder (GR) and sub-optimal responder (SOR) parasites. These variants were not randomly distributed but clustered in ~31 quantitative trait loci (QTLs), with little overlap in putative QTL position and gene content between the two countries. Published candidate ivermectin SOR genes were largely absent in these regions; QTLs differentiating GR and SOR worms were enriched for genes in molecular pathways associated with neurotransmission, development, and stress responses. Finally, single worm genotyping demonstrated that geographic isolation and genetic change over time (in the presence of drug exposure) had a significantly greater role in shaping genetic diversity than the evolution of SOR.This study is one of the first genome-wide association analyses in a parasitic nematode, and provides insight into the genomics of ivermectin response and population structure of O. volvulus. We argue that ivermectin response is a polygenically-determined quantitative trait (QT) whereby identical or related molecular pathways but not necessarily individual genes are likely to determine the extent of ivermectin response in different parasite populations. Furthermore, we propose that genetic drift rather than genetic selection of SOR is the underlying driver of population differentiation, which has significant implications for the emergence and potential spread of SOR within and between these parasite populations

On-the-fly Fast Mean-Field Model-Checking: Extended Version

A novel, scalable, on-the-fly model-checking procedure is presented to verify bounded PCTL properties of selected individuals in the context of very large systems of independent interacting objects. The proposed procedure combines on-the-fly model checking techniques with deterministic mean-field approximation in discrete time. The asymptotic correctness of the procedure is shown and some results of the application of a prototype implementation of the FlyFast model-checker are presented