Stochastic Series Research Articles

Ground states and dynamical properties of the S>1/2 quantum Heisenberg model on the 1/5-depleted square lattice

We study the $S>1/2$ antiferromagnetic Heisenberg model on the 1/5-depleted square lattice as a function of the ratio of the intraplaquette coupling to the interplaquette coupling. Using stochastic series expansion quantum Monte Carlo simulations, we numerically identify three quantum phases, including the dimer phase, N\'eel phase, and plaquette valence-bond-solid phase. We also obtain the accurate quantum critical points that belong to the $O$(3) universality class using the large-scale finite-size scaling. Most importantly, we study the dynamic spin structure factors of different phases, which can be measured by inelastic neutron scattering experiments. The low-energy excitations can be explained as triplons in the dimer phase and plaquette valence-bond-solid phase, while in the N\'eel phase, the more prominent magnon mode can be found as the spin magnitude increases. Furthermore, we find a broader continuum at smaller $S$, which may be the dynamical signature of nearly deconfined spinon excitations.

An optimizationless stochastic volterra series approach for nonlinear model identification

Volterra series is a widely used tool for identifying physical systems with polynomial nonlinearities. In this approach, the Volterra kernels expanded using Kautz functions can be identified using several techniques to optimize the filters’ poles. This methodology is very efficient when the system observations are not subject to high noise-induced variabilities (uncertainties). However, this optimization procedure may not be effective when the uncertainty level is increased since the optimal value might be susceptible to small perturbations. Seeking to overcome this weakness, the present work proposes a new stochastic method of identification based on the Volterra series, which does not solve an optimization problem. In this new approach, the Volterra kernels are described as stochastic processes. The parameters of Kautz filters are considered independent random variables so that their probability distribution captures the variabilities. The effectiveness of the new technique is tested experimentally in a nonlinear mechanical system. The results show that the identified stochastic Volterra kernels can reproduce the nonlinear dynamics characteristics and the data variability.

Quantum orders in the frustrated Ising model on the bathroom tile lattice

We determine the zero and finite temperature phase diagram of the fully frustrated quantum Ising model on the bathroom tile (4-8) lattice. The phase diagram exhibits a wealth of 2+1d physics, including 1. classical Coulomb dimer liquids of both square and triangular lattice types; 2. quantum order-by-disorder induced phases breaking $\mathbb{Z}_4$, $\mathbb{Z}_6$, and $\mathbb{Z}_8$ symmetries; 3. finite temperature Kosterlitz-Thouless (KT) phases floating over the $\mathbb{Z}_6$ and $\mathbb{Z}_8$ orders; and, 4. staircases of (in)-commensurate symmetry breaking phases at intermediate coupling. We establish this elaborate phase diagram using a combination of dimer model mapping, perturbation theory, Landau analysis and Stochastic Series Expansion Quantum Monte Carlo (QMC-SSE). Our results provide a baseline for studying frustrated magnetism with D-Wave architecture annealers, where the 4-8 lattice can be embedded naturally without `cloning', reducing the number of competing energy scales. Simulations with the D-Wave 2000Q demonstrate qualitative agreement with the high temperature portion of the phase diagram, but are unable to access the low temperature phases.

Sign-problem free quantum stochastic series expansion algorithm on a quantum computer

A quantum implementation of the Stochastic Series Expansion (SSE) Monte Carlo method is proposed, and is shown to offer significant advantages over classical implementations of SSE. In particular, for problems where classical SSE encounters the sign problem, the cost of implementing a Monte Carlo iteration scales only linearly with system size in quantum SSE, while it may scale exponentially with system size in classical SSE. In cases where classical SSE can be efficiently implemented, quantum SSE still offers an advantage by allowing for more general observables to be measured.

Methodology for the Development of Hybrid Renewable Energy Systems (HRES) with Pumped Storage and Hydrogen Production on Lemnos Island

The non-interconnected islands of Greece can benefit from the comprehensive use of RES to avoid water droughts and ensure energy autonomy. The present paper analyzes an HRES with two possible operating scenarios. Both of them include a wind park of 27.5 MW capacity, an 1175 m3/day desalination plant, and a 490,000 m3/day water tank in Lemnos, Greece. Regarding the wind power, 70% is used in the HRES, while the rest is channeled directly to the grid. The main difference comes down to how the wind energy is stored, either in the form of hydraulic energy or in the form of hydrogen. The lifespan of the system is 25 years, such as the produced stochastic series of rainfall, temperature, and wind of the area. Through the comparison of the operating scenarios, the following results arise: (i) the water needs of the island are fully covered and the irrigation needs have a reliability of 66%, in both scenarios. (ii) Considering the energy needs, the pumping storage seems to be the most reliable solution. (iii) However, depending on the amount of wind energy surplus, the use of hydrogen could produce more energy than the hydroelectric plant.

Quantum Monte Carlo simulation of spin-boson models using wormhole updates

We present an exact quantum Monte Carlo method for spin systems coupled to dissipative bosonic baths which makes use of nonlocal wormhole updates to simulate the retarded spin-flip interactions originating from an off-diagonal spin-boson coupling. The method is closely related to the stochastic series expansion and extends the scope of the global directed-loop updates to nonlocal moves through a world-line configuration. We test our method for the U(1)-symmetric two-bath spin-boson model, where the off-diagonal components of a spin-$1/2$ particle are coupled to identical independent baths with power-law spectra, and get a precise estimate of the critical coupling between the critical and the localized phase. Our method applies to impurity systems and lattice models in any spatial dimension coupled to bosonic modes with arbitrary spectral distributions.

Hosting Capacity Calculation Deploying a Hybrid Methodology: A Case Study Concerning the Intermittent Nature of Photovoltaic Distributed Generation and the Variable Nature of Energy Consumption in a Medium Voltage Distribution Network

The main methods employed for Hosting Capacity (HC) calculations are basically classified into deterministic, stochastic and time series. In this scenario, the authors herein propose a hybrid methodology, which shows efficiency and ease of implementation. Besides the method presented, it is also calculated a hosting capacity of a real feeder which was modeled and analyzed taking into consideration variations in load and power injected by distributed generation sources. The proposed hybrid method deploys just one time series with the feeder power demand data, which are easily obtained from the feeder’s origin substation. Low voltage loads were modeled by the ratio between their maximum demands and the feeder maximum demand, making easier to start up the grid model implementation. Hence, the advantages of the proposed methodology can be summarized in: (a) easy to obtain the input parameters; (b) agility in implementing the study; (c) higher processing speed and (d) results consistent with the time series method. Finally, in view of the advantages and obtained results, the proposed hybrid methodology shows itself as a promising and attractive tool for the studies of hosting capacity by the utilities.

Bulk and edge dynamics of a two-dimensional Affleck-Kennedy-Lieb-Tasaki model

We study the dynamical properties of both bulk and edge spins of a two-dimensional Affleck-Kennedy-Lieb-Tasaki (AKLT) model mainly by using the stochastic series expansion quantum Monte Carlo method with stochastic analytic continuation. In the deep AKLT phase, we obtain a spin spectrum with flat band, which is a strong evidence for a localized state. Through the spectrum analysis, we see a clear continuous phase transition from the AKLT phase to the N\'eel phase in the model, and the energy gap becomes closed at the corresponding momentum point. In comparison with linear spin-wave theory, the differences show that there are strong interactions among magnons at high energies. With open boundary condition, the gap of edge spins in the AKLT phase closes at both the $\Gamma$ point and the $\pi$ point interestingly to emerge into a flat-band-like Luttinger liquid phase, which can be explained by symmetry and perturbation approximation. This paper helps us to better understand the completely different dynamical behaviors of bulk and edge spins in the symmetry protected topological phase.

Auxiliary Particle Filtering Over Sensor Networks Under Protocols of Amplify-and-Forward and Decode-and-Forward Relays

In this paper, the particle filtering problem is investigated for a class of stochastic systems with multiple sensors under signal relays. To improve the performance of signal transmissions, a relay is deployed between each sensor and the remote filter. Both amplify-and-forward (AF) and decode-and-forward (DF) relays are considered under certain transmission protocols. Stochastic series are employed to describe multiplicative channel gains and additive transmission noises. Novel likelihood functions are derived based on the AF/DF relay models under different protocols. With the measurements collected from all the sensor nodes, a new centralized auxiliary particle filter (APF) is designed by resorting to the statistical information of the channel gains and transmission noises. Next, a consensus-based distributed APF is further established at each node that requires only locally available information. Finally, the effectiveness of the proposed filtering approach is demonstrated through target tracking simulation examples in different situations.

New framework for managing the water environmental capacity integrating the watershed model and stochastic algorithm

Integrated calculations of pollution load and water environmental capacity (WEC) are essential for effective water quality management. However, few studies have focused on the dynamic WEC and pollution load in a nonpoint source pollution (NPS)-dominant temperate monsoon watershed under changing rainfall conditions. In this study, a new framework based on the watershed model and WEC calculation with stochastic rainfall input (SR-WEC), was proposed to reveal the dynamic WEC and pollution load under changing rainfall conditions. Stochastic rainfall series was generated by a first-order Markov chain and gamma distribution, and further input into the Soil and Water Assessment Tool (SWAT) to explore the dynamic response of water quality to rainfall. The framework was applied to the Daning River watershed, Three Georges Reservoir Region, China. The results suggested that compared with the new SR-WEC, the traditional return period method with limited observed rainfall input would result in an underestimation of ideal WEC and NPS pollution load by 23% and 48% for TN and 48% and 51% for TP, respectively. Approximately 46% of the annual TN reduction and 51% of the annual TP reduction were concentrated from April to June in a relatively small area. The regression relationships between rainfall and the ideal WEC, pollution load and remnant WEC obtained by the SR-WEC were superior to those of the traditional method, with R2 values increasing from 0.005–0.797 to 0.718–0.989. Specific threshold (120 mm/month for the study area) was observed for the effect of rainfall on water quality, beyond which the remnant WEC of organic N would change from decreasing to increasing. The new framework proposed identifies the key periods and areas with consideration of uncertainty of rainfall on water quality, and provides basis for NPS pollution management.

Molecular Docking of the Cardenolides of Asclepias subulata in the Human p53 Protein Reveals an Interaction in the Cleft of the Y220C Mutant

Background and Objective: The objective of the present study is to use docking and ADME analysis to determine if the cardenolides of Asclepias subulata are potential stabilizing drugs of the p53-Y220C mutant. Materials and Methods: Two different receptors, wild-type p53, and the mutant p53-Y220C, were used for docking. Three independent stochastic series were performed, with 60,000 poses considered, and the 30 best poses were selected. ADME analysis was performed using SwissADME. Results: Docking experiments revealed that corotoxigenin 3-O-glucopyranoside and calotropin interact with the cleft, so they were considered potential stabilizers of the p53-Y220C mutant comparable to the control drug 9H5, which was able to predict a position very similar to that already reported in the crystallographic structure. The ADME predicted that calotropin and desglucouzarin have more favorable pharmacokinetic parameters. Both molecules are predicted to be absorbed from the GIT. Conclusion: Calotropin of A. subulata is predicted to be a potential drug for p53-Y220C, because it binds to the cleft of the mutant and has favorable pharmacokinetic parameters. Corotoxigenin 3- O-glucopyranoside also binds to the Y220C cleft, but had less favorable pharmacokinetic parameters. These results have a future impact since calotropin could be used for the treatment of some types of cancer.

Z2 topological order and first-order quantum phase transitions in systems with combinatorial gauge symmetry

We study a generalization of the two-dimensional transverse-field Ising model, combining both ferromagnetic and antiferromagnetic two-body interactions, that hosts exact global and local Z2 gauge symmetries. Using exact diagonalization and stochastic series expansion quantum Monte Carlo methods, we confirm the existence of the topological phase in line with previous theoretical predictions. Our simulation results show that the transition between the confined topological phase and the deconfined paramagnetic phase is of first-order, in contrast to the conventional Z2 lattice gauge model in which the transition maps onto that of the standard Ising model and is continuous. We further generalize the model by replacing the transverse field on the gauge spins with a ferromagnetic XX interaction while keeping the local gauge symmetry intact. We find that the Z2 topological phase remains stable, while the paramagnetic phase is replaced by a ferromagnetic phase. The topological-ferromagnetic quantum phase transition is also of first-order. For both models, we discuss the low-energy spinon and vison excitations of the topological phase and their avoided level crossings associated with the first-order quantum phase transitions.

Intrinsic Dimension of Path Integrals: Data-Mining Quantum Criticality and Emergent Simplicity

Quantum many-body systems are characterized by patterns of correlations that define highly-non trivial manifolds when interpreted as data structures. Physical properties of phases and phase transitions are typically retrieved via simple correlation functions, that are related to observable response functions. Recent experiments have demonstrated capabilities to fully characterize quantum many-body systems via wave-function snapshots, opening new possibilities to analyze quantum phenomena. Here, we introduce a method to data mine the correlation structure of quantum partition functions via their path integral (or equivalently, stochastic series expansion) manifold. We characterize path-integral manifolds generated via state-of-the-art Quantum Monte Carlo methods utilizing the intrinsic dimension (ID) and the variance of distances from nearest neighbors (NN): the former is related to dataset complexity, while the latter is able to diagnose connectivity features of points in configuration space. We show how these properties feature universal patterns in the vicinity of quantum criticality, that reveal how data structures {\it simplify} systematically at quantum phase transitions. This is further reflected by the fact that both ID and variance of NN-distances exhibit universal scaling behavior in the vicinity of second-order and Berezinskii-Kosterlitz-Thouless critical points. Finally, we show how non-Abelian symmetries dramatically influence quantum data sets, due to the nature of (non-commuting) conserved charges in the quantum case. Complementary to neural network representations, our approach represents a first, elementary step towards a systematic characterization of path integral manifolds before any dimensional reduction is taken, that is informative about universal behavior and complexity, and can find immediate application to both experiments and Monte Carlo simulations.

The Truncated Burr X-G Family of Distributions: Properties and Applications to Actuarial and Financial Data.

In this article, the “truncated-composed” scheme was applied to the Burr X distribution to motivate a new family of univariate continuous-type distributions, called the truncated Burr X generated family. It is mathematically simple and provides more modeling freedom for any parental distribution. Additional functionality is conferred on the probability density and hazard rate functions, improving their peak, asymmetry, tail, and flatness levels. These characteristics are represented analytically and graphically with three special distributions of the family derived from the exponential, Rayleigh, and Lindley distributions. Subsequently, we conducted asymptotic, first-order stochastic dominance, series expansion, Tsallis entropy, and moment studies. Useful risk measures were also investigated. The remainder of the study was devoted to the statistical use of the associated models. In particular, we developed an adapted maximum likelihood methodology aiming to efficiently estimate the model parameters. The special distribution extending the exponential distribution was applied as a statistical model to fit two sets of actuarial and financial data. It performed better than a wide variety of selected competing non-nested models. Numerical applications for risk measures are also given.

Calculation and realization of new method grey residual error correction model.

Aiming at the problem of prediction accuracy of stochastic volatility series, this paper proposes a method to optimize the grey model(GM(1,1)) from the perspective of residual error. In this study, a new fitting method is firstly used, which combines the wavelet function basis and the least square method to fit the residual data of the true value and the predicted value of the grey model(GM(1,1)). The residual prediction function is constructed by using the fitting method. Then, the prediction function of the grey model(GM(1,1)) is modified by the residual prediction function. Finally, an example of the wavelet residual-corrected grey prediction model (WGM) is obtained. The test results show that the fitting accuracy of the wavelet residual-corrected grey prediction model has irreplaceable advantages.

Quantum-critical properties of the long-range transverse-field Ising model from quantum Monte Carlo simulations

The quantum-critical properties of the transverse-field Ising model with algebraically decaying interactions are investigated by means of stochastic series expansion quantum Monte Carlo, on both the one-dimensional linear chain and the two-dimensional square lattice. We extract the critical exponents $\nu$ and $\beta$ as a function of the decay exponent of the long-range interactions. For ferromagnetic Ising interactions, we resolve the limiting regimes known from field theory, ranging from the nearest-neighbor Ising to the long-range Gaussian universality classes, as well as the intermediate regime with continuously varying critical exponents. In the long-range Gaussian regime, we treat the effect of dangerous irrelevant variables on finite-size scaling forms. For antiferromagnetic and therefore competing Ising interactions, the stochastic series expansion algorithm displays growing auto-correlation times leading to a reduced performance. Nevertheless, our results are consistent with the nearest-neighbor Ising universality for all investigated interaction ranges both on the linear chain and the square lattice.

Predicting springback variation and process-reliable tolerance limits of outer car-body panels by stochastic sheet metal forming simulation

Modern car-body design entails increasing requirements for the dimensional accuracy of outer car-body panels. However, tolerance limits to be met in this regard are based on specifications from component engineering aimed at ensuring dimensional accuracy of the product, less on real structural springback behaviour of outer car-body panels. Process-reliable tolerance limits for outer car-body panels can be characterized by a bandwidth in springback variation caused by fluctuations in material characteristics and process parameters during production. Differences between assumptions from component engineering and real structural springback behaviour of outer car-body panels thus leads to avoidable iterative corrections in die manufacturing and following processes. Therefore, the goal of this research work presented in this paper is to predict springback variation potentially occurring during production already in the virtual design stage of a car-body and hence set process-reliable tolerance limits. Stochastic sheet metal forming simulation is used for prediction of springback variation. Here, deterministic multi-stage springback simulation of a sidewall panel is extended by stochastic variation of material properties and process parameters. Simulation results are validated by measurement reports from series production. Results presented show strong fit in characteristics of springback variation between stochastic simulation and series measurement reports. In future, stochastic simulation results can be fed back into component engineering, making die manufacturing and following joining and assembly processes more effective.

Semantically predictable input streams impede gaze-orientation to surprising locations

When available, people use prior knowledge to predict dimensions of future events such as their location and semantic features. However, few studies have examined how multi-dimensional predictions are implemented, and mechanistic accounts are absent. Using eye tracking, we evaluated whether predictions of target-location and target-category interact during the earliest stages of orientation. We presented stochastic series so that across four conditions, participants could predict either the location of the next target-image, its semantic category, both dimensions, or neither. Participants observed images in absence of any task involving their semantic content. We modeled saccade latencies using ELATER, a rise-to-threshold model that accounts for accumulation rate (AR), variance of AR over trials, and variance of decision baseline. The main findings were: 1) AR scaled with the degree of surprise associated with a target's location; 2) predictability of semantic-category hindered saccade latencies, suggesting a bottleneck in implementing joint predictions; 3) saccades to targets that satisfied semantic expectations were associated with greater AR-variance than saccades to semantically-surprising images, consistent with a richer repertoire of early evaluative processes for semantically-expected images. Predictability of target-category also impacted gaze pre-positioning prior to target presentation. The results indicate a strong interaction between foreknowledge of object location and semantics during stimulus-guided saccades, and suggest statistical regularities in an input stream can also impact anticipatory, non-stimulus-guided processes.

Breathing kagome XY quantum magnet with four-site ring exchange

We study the impact of trimerization (breathing) of the nearest-neighbor (NN) exchange on the planar XY spin-1/2 ferromagnet on the kagome lattice, including additional four-site ring exchange. For uniform NN exchange, this model has previously been shown to transit from a long-range ordered ferromagnet into a Z2 quantum spin liquid by virtue of the ring exchange. Using quantum Monte-Carlo calculations, based on the stochastic series expansion, we present results for the spin stiffness, the quantum phase diagram, the longitudinal static, as well as the transverse dynamic structure factor. Our results corroborate 3D XY universality also at finite trimerization and suggest a simple continuation of the quantum critical point of the uniform case into a line in terms of rescaled exchange parameters. Moreover, at any trimerization and in the ordered phase the elementary excitations can be understood very well in terms of linear spin wave theory, while beyond the critical line, in the spin liquid phase we find signatures of spinon continua.

Life cycle resilience quantification and enhancement of power distribution systems: A risk-based approach

Distribution systems in the US are commonly supported by wood utility poles. Since wood poles may experience substantial decay rates, current standards specify a strength-based maintenance program for pole replacement regardless of the poles’ vulnerability and importance in the system. While state-of-the-art methods have developed risk-based metrics to guide system hardening decisions, such metrics are analyzed for the current conditions of the system. In this context, the potential of a stochastic series of hazards over extended horizons and the subsequent effects on the resilience of systems have been largely neglected. To address these limitations, a risk-based methodology is proposed for quantifying the life cycle resilience of power distribution systems. To project pole vulnerability, a recursive approach is developed that captures the stochasticity of precedent failures and subsequent corrective actions over extended horizons. Furthermore, a risk-based replacement index called Expected Outage Reduction (EOR) is introduced that estimates the expected power outage reduction if an existing pole is replaced by a new pole. The application of the proposed method for life cycle resilience analysis and management of a realistic distribution system subjected to stochastic hurricanes indicates that EOR can improve the cumulative life cycle resilience by up to 22.3% over 70 years.