Monte Carlo Data Research Articles

A response-matrix-centred approach to presenting cross-section measurements

The current canonical approach to publishing cross-section data is to unfold the reconstructed distributions. Detector effects like efficiency and smearing are undone mathematically, yielding distributions in true event properties. This is an ill-posed problem, as even small statistical variations in the reconstructed data can lead to large changes in the unfolded spectra. This work presents an alternative or complementary approach: the response-matrix-centred forward-folding approach. It offers a convenient way to forward-fold model expectations in truth space to reconstructed quantities. These can then be compared to the data directly, similar to what is usually done with full detector simulations within the experimental collaborations. For this, the detector response (efficiency and smearing) is parametrised as a matrix. The effects of the detector on the measurement of a given model is simulated by simply multiplying the binned truth expectation values by this response matrix. Systematic uncertainties in the detector response are handled by providing a set of matrices according to the prior distribution of the detector properties and marginalising over them. Background events can be included in the likelihood calculation by giving background events their own bins in truth space. To facilitate a straight-forward use of response matrices, a new software framework has been developed: the Response Matrix Utilities (\\ReMU). \\ReMU is a Python package distributed via the Python Package Index. It only uses widely available, standard scientific Python libraries and does not depend on any custom experiment-specific software. It offers all methods needed to build response matrices from Monte Carlo data sets, use the response matrix to forward-fold truth-level model predictions, and compare the predictions to real data using Bayesian or frequentist statistical inference.

Event Studies and Outlier Returns: Symptoms, Consequences and Treatment

This paper makes specifics contributions in the methodology of event studies. First, it develops a financial econometrics framework for understanding, measuring and testing the impact of outlier returns on the estimated parameters of stock return models. Second, it presents a maximum likelihood robust estimation method that enables the decomposition of a firm’s stock returns into regular and outlier returns for the purpose of computing robust or outlier resistant CAR statistics. Third, it presents analytical results on how outliers in the estimation sample affect OLS-CAR statistics. Results based on extensive Monte Carlo and actual data simulations, depict that outliers in the estimation sample affect adversely and significantly the performance of the OLS-CAR statistics in event studies. Outliers, however, do not impair the forecasting ability of the robust-CAR statistics introduced in this paper.

Approximate expression for the ground-state energy of the two- and three-dimensional Hubbard model at arbitrary filling obtained from dimensional scaling

We generalize the linear discrete dimensional scaling approach for the repulsive Hubbard model to obtain a nonlinear scaling relation that yields accurate approximations to the ground-state energy in both two and three dimensions, as judged by comparison to auxiliary-field quantum Monte Carlo (QMC) data. Predictions are made for the per-site ground-state energies in two and three dimensions for n (filling factor) and U (Coulomb interaction) values for which QMC data are currently unavailable.

The three-body cluster energy for the [formula omitted] asymmetric [formula omitted] matter in the [formula omitted] formalism

The equation of state (EOS) of the isospin asymmetric nucleonic matter (IASM) is studied in the Lowest Order Constrained Variational (LOCV) formalism, using the AV18 two-body potential with a density-dependent three-body interaction (TBI), which was proposed by Lagaris and Pandharipande (LP) in 1981. In the LOCV framework, an adjustment mechanism is introduced for finding the appropriate parameters of the TBI. It is shown that, assuming the TBI, the corresponding LOCV symmetric nuclear (pure neutron) matter results fairly agree with those of Fermi Hypernetted Chain (FHNC). Also, the contribution of the averaged three-body cluster (TBC) energy is evaluated, at different proton to neutron ratios R. Employing the TBI, up to ρ=0.5 fm−3, the TBC energy ranges from −6 to 6 MeV per particle which considerably changes the IASMEOS, especially at low densities. Moreover, employing the TBI, the LOCVIASM state-averaged correlation functions (effective potentials) and the nucleon–nucleon distribution functions (NNDF) are reported. It is illustrated that, by increasing the density (ratio R), the impact of the TBI becomes much more evident. Finally, it should be noted that, the IASMFHNC and Monte Carlo (MC) data are not available for comparison.

Thermal tensor renormalization group simulations of square-lattice quantum spin models

In this work, we benchmark the well-controlled and numerically accurate exponential thermal tensor renormalization group (XTRG) in the simulation of interacting spin models in two dimensions. Finite temperature introduces a thermal correlation length, which justifies the analysis of finite system size for the sake of numerical efficiency. In this paper we focus on the square lattice Heisenberg antiferromagnet (SLH) and quantum Ising models (QIM) on open and cylindrical geometries up to width $W=10$. We explore various one-dimensional mapping paths in the matrix product operator (MPO) representation, whose performance is clearly shown to be geometry dependent. We benchmark against quantum Monte Carlo (QMC) data, yet also the series-expansion thermal tensor network results. Thermal properties including the internal energy, specific heat, and spin structure factors, etc., are computed with high precision, obtaining excellent agreement with QMC results. XTRG also allows us to reach remarkably low temperatures. For SLH we obtain at low temperature an energy per site $u_g^*\simeq -0.6694(4)$ and a spontaneous magnetization $m_S^*\simeq0.30(1)$, which is already consistent with the ground state properties. We extract an exponential divergence vs. $T$ of the structure factor $S(M)$, as well as the correlation length $\xi$, at the ordering wave vector $M=(\pi,\pi)$, which represents the renormalized classical behavior and can be observed over a narrow but appreciable temperature window, by analysing the finite-size data by XTRG simulations. For the QIM with a finite-temperature phase transition, we employ several thermal quantities, including the specific heat, Binder ratio, as well as the MPO entanglement to determine the critical temperature $T_c$.

Modulation of gold nanoparticle mediated radiation dose enhancement through synchronization of breast tumor cell population.

The incorporation of high atomic number materials such as gold nanoparticles (GNPs) into tumor cells is being tested to enhance the local radiotherapy (RT) dose. It is also known that the radiosensitivity of tumor cells depends on the phase of their cell cycle. Triple combination of GNPs, phase of tumor cell population, and RT for improved outcomes in cancer treatment. We used a double-thymidine block method for synchronization of the tumor cell population. GNPs of diameters 17 and 46 nm were used to capture the size dependent effects. A radiation dose of 2 Gy with 6 MV linear accelerator was used to assess the efficacy of this proposed combined treatment. A triple negative breast cancer cell line, MDA-MB-231 was chosen as the model cell line. Monte Carlo (MC) calculations were done to predict the GNP-mediated cell death using the experimental GNP uptake data. There was a 1.5- and 2- fold increase in uptake of 17 and 46 nm GNPs in the synchronized cell population, respectively. A radiation dose of 2 Gy with clinically relevant 6 MV photons resulted in a 62 and 38 % enhancement in cell death in the synchronized cell population with the incorporation of 17 and 46 nm GNPs, respectively. MC data supported the experimental data, but to a lesser extent. A triple combination of GNPs, cell cycle synchronization, and RT could pave the way to enhance the local radiation dose while minimizing side effects to the surrounding healthy tissue. This is the first study to show that the combined use of GNPs, phase of tumor cell population, and RT could enhance tumor cell death.

Tail-regression estimator for heavy-tailed distributions of known tail indices and its application to continuum quantum Monte Carlo data.

Standard statistical analysis is unable to provide reliable confidence intervals on expectation values of probability distributions that do not satisfy the conditions of the central limit theorem. We present a regression-based estimator of an arbitrary moment of a probability distribution with power-law heavy tails that exploits knowledge of the exponents of its asymptotic decay to bypass this issue entirely. Our method is applied to synthetic data and to energy and atomic force data from variational and diffusion quantum Monte Carlo calculations, whose distributions have known asymptotic forms [J.R. Trail, Phys. Rev. E 77, 016703 (2008)PLEEE81539-375510.1103/PhysRevE.77.016703; A. Badinski et al., J. Phys.: Condens. Matter 22, 074202 (2010)JCOMEL0953-898410.1088/0953-8984/22/7/074202]. We obtain convergent, accurate confidence intervals on the variance of the local energy of an electron gas and on the Hellmann-Feynman force on an atom in the all-electron carbon dimer. In each of these cases the uncertainty on our estimator is 45% and 60 times smaller, respectively, than the nominal (ill-defined) standard error.

Ab initio path integral Monte Carlo approach to the static and dynamic density response of the uniform electron gas

In a recent Letter [T. Dornheim et al., Phys. Rev. Lett. 121, 255001 (2018)] we have presented ab initio results for the dynamic structure factor $S(\mathbf{q},\ensuremath{\omega})$ of the uniform electron gas for conditions ranging from the warm dense matter regime to the strongly correlated electron liquid. This was achieved on the basis of exact path integral Monte Carlo data by stochastically sampling the dynamic local field correction $G(\mathbf{q},\ensuremath{\omega})$. In this paper we introduce in detail this reconstruction method and provide several practical demonstrations. Moreover, we thoroughly investigate the associated imaginary-time density-density correlation function $F(\mathbf{q},\ensuremath{\tau})$. The latter also gives us access to the static density-response function $\ensuremath{\chi}(\mathbf{q})$ and static local field correction $G(\mathbf{q})$, which are compared to standard dielectric theories like the widespread random phase approximation. In addition, we study the high-frequency limit of $G(\mathbf{q},\ensuremath{\omega})$ and provide extensive results for the dynamic structure factor for different densities and temperatures. Finally, we discuss the implications of our findings for warm dense matter research and the interpretation of experiments.

Large Mpemba-like effect in a gas of inelastic rough hard spheres.

We report the emergence of a giant Mpemba effect in the uniformly heated gas of inelastic rough hard spheres: The initially hotter sample may cool sooner than the colder one, even when the initial temperatures differ by more than one order of magnitude. In order to understand this behavior, it suffices to consider the simplest Maxwellian approximation for the velocity distribution in a kinetic approach. The largeness of the effect stems from the fact that the rotational and translational temperatures, which obey two coupled evolution equations, are comparable. Our theoretical predictions agree very well with molecular dynamics and direct simulation Monte Carlo data.

Holographic quantum critical response from 6 derivative theory

The holographic quantum critical (QC) response from 6 derivative theory is studied in this paper. We find that once the higher derivative (HD) terms are introduced, to fit quantum Monte Carlo (QMC) data from O(2) quantum critical phase (QCP), a rescaling for any Δ is needed. Also, we study the real frequency conductivity. We find that the scalar profile dual to the relevant operator has more evident effect on both the low frequency and the intermediate frequency than the scalar profile dual to the irrelevant operator. Finally, we study the electromagnetic (EM) duality. We confirm the robustness that the irrelevant operator help to the particle-vortex duality holds more well with the change of the sign of the coupling parameter.

The role of radiation-induced charge imbalance on the dose-response of a commercial synthetic diamond detector in small field dosimetry.

PurposeDiscrepancy between experimental and Monte Carlo simulated dose–response of the microDiamond (mD) detector (type 60019, PTW Freiburg, Germany) at small field sizes has been reported. In this work, the radiation‐induced charge imbalance in the structural components of the detector has been investigated as the possible cause of this discrepancy.Materials and methodsOutput ratio (OR) measurements have been performed using standard and modified versions of the mD detector at nominal field sizes from 6 mm × 6 mm to 40 mm × 40 mm. In the first modified mD detector (mD_reversed), the type of charge carriers collected is reversed by connecting the opposite contact to the electrometer. In the second modified mD detector (mD_shortened), the detector's contacts have been shortened. The third modified mD detector (mD_noChip) is the same as the standard version but the diamond chip with the sensitive volume has been removed. Output correction factors were calculated from the measured OR and simulated using the EGSnrc package. An adapted Monte Carlo user‐code has been used to study the underlying mechanisms of the field size‐dependent charge imbalance and to identify the detector's structural components contributing to this effect.ResultsAt the smallest field size investigated, the OR measured using the standard mD detector is >3% higher than the OR obtained using the modified mD detector with reversed contact (mD_reversed). Combining the results obtained with the different versions of the detector, the OR have been corrected for the effect of radiation imbalance. The OR obtained using the modified mD detector with shortened contacts (mD_shortened) agree with the corrected OR, all showing an over‐response of less than 2% at the field sizes investigated. The discrepancy between the experimental and simulated output correction factors has been eliminated after accounting for the effect of charge imbalance.Discussions and conclusionsThe role of radiation‐induced charge imbalance on the dose–response of mD detector in small field dosimetry has been studied and quantified. It has been demonstrated that the effect is significant at small field sizes. Multiple methods were used to quantify the effect of charge imbalance with good agreement between Monte Carlo simulations and experimental results obtained with modified detectors. When this correction is applied to the Monte Carlo data, the discrepancy from experimental data is eliminated. Based on the detailed component analysis using an adapted Monte Carlo user‐code, it has been demonstrated that the effect of charge imbalance can be minimized by modifying the design of the detector's contacts.

Condensation of eigen microstate in statistical ensemble and phase transition

In a statistical ensemble with $M$ microstates, we introduce an $M \times M$ correlation matrix with the correlations between microstates as its elements. Using eigenvectors of the correlation matrix, we can define eigen microstates of the ensemble. The normalized eigenvalue by $M$ represents the weight factor in the ensemble of the corresponding eigen microstate. In the limit $M \to \infty$, weight factors go to zero in the ensemble without localization of microstate. The finite limit of weight factor when $M \to \infty$ indicates a condensation of the corresponding eigen microstate. This indicates a phase transition with new phase characterized by the condensed eigen microstate. We propose a finite-size scaling relation of weight factors near critical point, which can be used to identify the phase transition and its universality class of general complex systems. The condensation of eigen microstate and the finite-size scaling relation of weight factors have been confirmed by the Monte Carlo data of one-dimensional and two-dimensional Ising models.

Improvement in the 3D shower shapes description in the Monte Carlo simulation for a lead-scintillating fiber electromagnetic calorimeter

The lead-scintillating fiber electromagnetic calorimeter (ECAL) of the Alpha Magnetic Spectrometer measures the energy of positrons/electrons and separates them from hadrons. The electromagnetic shower shapes from Monte Carlo (MC) simulation and data show disagreement. Tuning the MC to make the shower shapes from MC and data agree with each other. The tuning is based on a 3D electromagnetic shower model. After tuning, the electromagnetic shower shapes are well described by MC up to TeV. As a result, the output of ECAL electron/proton separation estimator, ECAL BDT, shows that MC and data are in good agreement. The proton rejection power of the ECAL BDT trained with MC electron samples is improved by a factor of 5 at $$\sim \,800\,\hbox {GeV}$$ compared to the one trained with data.

A control-function approach to correct for endogeneity in discrete choice models estimated on SP-off-RP data and contrasts with an earlier FIML approach by Train & Wilson

It is common practice to build Stated Preference (SP) attributes and alternatives from observed Revealed Preference (RP) choices with a view to increasing realism. While many surveys pivot all alternatives around an observed choice, others use more adaptive approaches in which changes are made depending on what alternative was chosen in the RP setting. For example, in SP-off-RP data, the alternative chosen in the RP setting is worsened in the SP setting and other alternatives are improved to induce a change in behaviour. This facilitates the creation of meaningful trade-offs or tipping points but introduces endogeneity. This source of endogeneity was largely ignored until Train and Wilson (T&W) proposed a full information maximum likelihood (FIML) solution that can be implemented with simulation. In this article, we propose a limited information maximum likelihood (LIML) approach to address the SP-off-RP problem using a method which does not need simulation, can be applied with standard software and uses data that is already available for the stated problem. The proposed method is an application of the control-function (CF) method to correct for endogeneity in discrete choice models, using the RP attributes as instrumental variables. We discuss the theoretical and practical advantages and disadvantages of the CF and T&W methods and illustrate them using Monte Carlo and real data. Results show that, while the T&W method may be more efficient in theory, it may however fail to retrieve consistent estimators when it does not account properly for the data generation process if, e.g., an exogenous source of correlation among the SP choice tasks exists. On the other hand, the CF is more robust, i.e. less sensitive, to the data generation process assumptions, and is considerably easier to apply with standard software and does not require simulation, facilitating its adoption and the more extensive use of SP-off-RP data.

The accuracy of the theories based on statistical physics for the thermodynamic modeling of state parameters of dense pure gases (fluids)

A comparison of the accuracy of calculations of the parameters of the state of dense supercritical gases (fluids) using the equations of state (EOS), obtained using the three best one fluid theories HMSA/C, MRCSR and KLRR-T, based on the given potentials of intermolecular interactions and the laws of statistical mechanics is carried out. The best agreement of the calculated state parameters with Monte Carlo data was obtained for the EOS based on the HMSA/C and KLRR-T theories.

Assessment of Density Functional Theory in Predicting Interaction Energies between Water and Polycyclic Aromatic Hydrocarbons: from Water on Benzene to Water on Graphene.

The interactions of water with polycyclic aromatic hydrocarbons, from benzene to graphene, are investigated using various exchange-correlation functionals selected across the hierarchy of density functional theory (DFT) approximations. The accuracy of the different functionals is assessed through comparisons with random phase approximation (RPA) and coupled-cluster with single, double, and perturbative triple excitations [CCSD(T)] calculations. Diffusion Monte Carlo (DMC) data reported in the literature are also used for comparison. Relatively large variations are found in interaction energies predicted by different DFT models, with GGA functionals underestimating the interaction strength for configurations with the water oxygen pointing toward the aromatic molecules. The meta-GGA B97M-rV and range-separated hybrid, meta-GGA ωB97M-V functionals provide nearly quantitative agreement with CCSD(T) values for the water-benzene, water-coronene, and water-circumcoronene dimers, while RPA and DMC predict interaction energies that differ by up to ∼1 kcal/mol and ∼0.4 kcal/mol from the corresponding CCSD(T) values, respectively. Similar trends among GGA, meta-GGA, and hybrid functionals are observed for larger polycyclic aromatic hydrocarbons. By performing absolutely localized molecular orbital energy decomposition analyses (ALMO-EDA), it is found that, independently of the number of carbon atoms and exchange-correlation functional, the dominant contributions to the interaction energies between water and polycyclic aromatic hydrocarbon molecules are the electrostatic and dispersion terms while polarization and charge transfer effects are negligibly small. Calculations carried out with GGA and meta-GGA functionals indicate that, as the number of carbon atoms increases, the interaction energies slowly converge to the corresponding values obtained for an infinite graphene sheet.

Online discrete choice models: Applications in personalized recommendations

This paper presents a framework for estimating and updating user preferences in the context of app-based recommender systems. We specifically consider recommender systems which provide personalized menus of options to users. A Hierarchical Bayes procedure is applied in order to account for inter- and intra-consumer heterogeneity, representing random taste variations among individuals and among choice situations (menus) for a given individual, respectively. Three levels of preference parameters are estimated: population-level, individual-level and menu-specific. In the context of a recommender system, the estimation of these parameters is repeated periodically in an offline process in order to account for trends, such as changing market conditions. Furthermore, the individual-level parameters are updated in real-time as users make choices in order to incorporate the latest information from the users. This online update is computationally efficient which makes it feasible to embed it in a real-time recommender system. The estimated individual-level preferences are stored for each user and retrieved as inputs to a menu optimization model in order to provide recommendations. The proposed methodology is applied to both Monte-Carlo and real data. It is observed that the online update of the parameters is successful in improving the parameter estimates in real-time. This framework is relevant to various recommender systems that generate personalized recommendations ranging from transportation to e-commerce and online marketing, but is particularly useful when the attributes of the alternatives vary over time.

Application of a directional palladium-103 brachytherapy device on a curved surface.

The directional planar palladium-103 LDR device (CivaSheet ) may be used for intraoperative implantation at the interface between the tumor site and healthy tissue. Its dosimetric properties have been studied in the ideal case of application on a flat surface. The dosimetric impact of implanting this highly directional device on a curved surface that may be encountered in clinical treatments is analyzed. CivaSheet is designed as an array of directional palladium-103 sources (CivaDots). From the postoperative computed tomography (CT) scans of three patients, the shape of each implanted CivaSheet was reconstructed. In order to obtain a realistic estimate of the distribution of curvatures, the mean radius of curvature at the location of each CivaDot was calculated. A Monte Carlo simulation (FLUKA) of a single CivaDot was designed, based upon published geometry and material specifications. Both the radial dose function analog and the two-dimensional anisotropy function analog for the CivaDot were validated in comparison with film measurements and benchmarked to published Monte Carlo data. A value for the dose-rate constant Λ=0.587(19)cGy/h/U for a CivaDot source in water was calculated as well. Knowledge of the dose distribution in the vicinity of each source allowed the dose at any point around CivaSheets of different curvatures and orientations to be calculated. The local radius of curvature was found to be primarily between 2 and 8cm in all three patient implants. On the unshielded side of an inward-facing curved CivaSheet implant of radius 2cm, the calculated dose at 0.5cm depth exceeded the prescribed dose by ∼20%, while on the shielded side the dose increased by a factor of two, thus compromising the shielding efficiency of the original design. On the unshielded side of an outward-facing curved implant, the dose at 0.5cm depth decreased by ∼20%. When tumor bed curvature can be estimated from the preplanning CT scan, the results from this study provide quantitative guide for modifying the source strength to achieve the desired clinical results. In many intraoperative cases, however, accurate preplanning based on surface curvature may not be practical. In such situations, knowledge of the dosimetric impact of the surface curvature provides motivation for avoiding implantation geometries that can lead to either over/underdosing the target, or excess dose to healthy tissue.

Modeling of Knudsen Layer Effects in the Micro-Scale Backward-Facing Step in the Slip Flow Regime

The effect of the Knudsen layer in the thermal micro-scale gas flows has been investigated. The effective mean free path model has been implemented in the open source computational fluid dynamics (CFD) code, to extend its applicability up to slip and early transition flow regime. The conventional Navier-Stokes constitutive relations and the first-order non-equilibrium boundary conditions are modified based on the effective mean free path, which depends on the distance from the solid surface. The predictive capability of the standard ‘Maxwell velocity slip—Smoluchwoski temperature jump’ and hybrid boundary conditions ‘Langmuir Maxwell velocity slip—Langmuir Smoluchwoski temperature jump’ in conjunction with the Knudsen layer formulation has been evaluated in the present work. Simulations are carried out over a nano-/micro-scale backward facing step geometry in which flow experiences adverse pressure gradient, separation and re-attachment. Results are validated against the direct simulation Monte Carlo (DSMC) data, and have shown significant improvement over the existing CFD solvers. Non-equilibrium effects on the velocity and temperature of gas on the surface of the backward facing step channel are studied by varying the flow Knudsen number, inlet flow temperature, and wall temperature. Results show that the modified solver with hybrid Langmuir based boundary conditions gives the best predictions when the Knudsen layer is incorporated, and the standard Maxwell-Smoluchowski can accurately capture momentum and the thermal Knudsen layer when the temperature of the wall is higher than the fluid flow.

Persistence length convergence and universality for the self-avoiding random walk

In this study, we show the convergence and new properties of persistence length, , for the self-avoiding random walk model (SAW) using Monte Carlo data. We generate high precision estimates of several conformational quantities with a pivot algorithm for the square, hexagonal, triangular, cubic and diamond lattices with path lengths of 103 steps. For each lattice, we accurately estimate the asymptotic limit , which corroborates the convergence of to a constant value, and allows us to check the universality on the curves. Based on the estimates we make an ansatz for dependency with lattice cell and spatial dimension, we also find a new geometric interpretation for the persistence length.