Monte Carlo Data Research Articles

Hierarchical Missing Data and Multivariate Behrens–Fisher Problem

This article firstly defines hierarchical data missing pattern, which is a generalization of monotone data missing pattern. Then multivariate Behrens–Fisher problem with hierarchical missing data is considered to illustrate that how ideas in dealing with monotone missing data can be extended to deal with hierarchical missing pattern. A pivotal quantity similar to the Hotelling T 2 is presented, and the moment matching method is used to derive its approximate distribution which is for testing and interval estimation. The precision of the approximation is illustrated through Monte Carlo data simulation. The results indicate that the approximate method is very satisfactory even for moderately small samples.

Nonequilibrium temperature, entropy production, and bulk viscosity of one-dimensional normal shock waves.

The nonequilibrium temperature in the kinetic theory of gases is reexamined and an alternative definition of the temperature in terms of the local equilibrium distribution function is proposed. The alternative definition introduces a new physical quantity, 'exoenergy,' which represents the nonequilibrium nature of thermodynamic systems. The internal energy equation is split into two equations, the temperature equation and the exoenergy equation. In order to rationalize the equation splitting, the nonequilibrium thermodynamics is considered introducing the nonequilibrium entropy phenomenologically. The proposed temperature equation resolves the overshooting anomaly of temperature profiles of the Monte Carlo data for one-dimensional normal shock waves. The exoenergy equation makes the theory self-consistent and gives the entropy production of shock waves in closed form. The theory gives a general form of the shock wave equation and the general relation of the bulk viscosity to the shear viscosity and the heat conductivity of dilute monatomic gases.

Berezinskii-Kosterlitz-Thouless transitions in two-dimensional lattice SO(Nc) gauge theories with two scalar flavors

We study the phase diagram and critical behavior of a two-dimensional lattice $\mathrm{SO}({N}_{c})$ gauge theory (${N}_{c}\ensuremath{\ge}3$) with two scalar flavors, obtained by partially gauging a maximally $\mathrm{O}(2{N}_{c})$ symmetric scalar model. The model is invariant under local $\mathrm{SO}({N}_{c})$ and global O(2) transformations. We show that, for any ${N}_{c}\ensuremath{\ge}3$, it undergoes finite-temperature Berezinskii-Kosterlitz-Thouless (BKT) transitions, associated with the global Abelian O(2) symmetry. The transition separates a high-temperature disordered phase from a low-temperature spin-wave phase where correlations decay algebraically (quasi-long range order). The critical properties at the finite-temperature BKT transition and in the low-temperature spin-wave phase are determined by means of a finite-size scaling analysis of Monte Carlo data.

Covid-19 transmission modelling of students returning home from university

ABSTRACT We provide an open-source model to estimate the number of secondary Covid-19 infections caused by potentially infectious students returning from university to private homes with other occupants. Using a Monte-Carlo method and data derived from UK sources, we predict that an infectious student would, on average, infect 0.94 other household members. Or, as a rule of thumb, each infected student would generate (just less than) one secondary within-household infection. The total number of secondary cases for all returning students is dependent on the virus prevalence within each student population at the time of their departure from campus back home. Although the proposed estimation method is general and robust, the results are sensitive to the input data. We provide Matlab code and a helpful online app (http://bit.ly/Secondary_infections_app) that can be used to estimate numbers of secondary infections based on local parameter values. This can be used worldwide to support policy making.

The Role of Forced Oscillators of Coupled Circuits in Radiation Physics: New Linear Accelerator Design Improving Tomo-Scanning Technology (Radiotherapy and CT), Heisenberg-Euler Scatter, and Extension to Bremsstrahlung with GeV Electrons

The quantization of circuits has received to be rather attractive in domains of solid state—molecular—and biophysics, since the quanta referred to as Q-bits play a significant role in the design of the quantum computer and entangled structures. Quantized circuits cannot be applied without modifications, since the energy differences are not equidistant and the polarization of the excited states has to be accounted for having particular importance for the creation of virtual states. Applications of the presented theory are scanning methods in radiotherapy without multi-leaf collimators, which may be realized in tomo-scanning radiotherapy and in the keV domain, which provides a new design of CT. The problem of lateral scatter in the target and energy storage by heat production is significantly reduced by a multilayer system with focusing the impinging electrons at the walls and by a magnetic field. The verification of the Heisenberg-Euler scatter of crossing beams of 9 MV is a central problem of photon physics and can be solved by the new bremsstrahlung technique. A comparison with GEANT 4 Monte-Carlo data indicates that the presented method also works in the GeV domain, and a multi-target can improve the bremsstrahlung yield. GEANT 4 provides the spatial distribution, whereas the virtual oscillator states only show the created energy spectrum. In every case, the exploitation yield can be drastically improved by the superiority of the focused multitarget system compared to a single standard target, and the door to new technologies is opened.

Towards Dynamic Isochrone Mapping Accounting for Uncertainty

Isochrone Mapping has been used since the late 19th century as a planning and visualization tool in various domains, such as transport planning and hydrology. In the past, isochrone calculation was based mainly on static properties and therefore also yielded static maps. This resulted in a potentially significant — and at the same time unquantifiable — degree of uncertainty. Today however, advances both in information technology and in the availability of input data allow much more nuanced views on the subject. This paper gives an overview of work on dynamic factors that contribute to uncertainty in isochrone calculation and mapping. Various application scenarios and their constraints are discussed, and open research challenges and possibilities identified. Finally, we present preliminary results from a practical approach to quantifying uncertainties in isochrone calculation for motorized individual transport based on Monte Carlo simulations and data from open routing APIs.

Non-monotonic Mpemba effect in binary molecular suspensions

The Mpemba effect is a phenomenon in which an initially hotter sample cools sooner. In this paper, we show the emergence of a non-monotonic Mpemba-like effect in a molecular binary mixture immersed in a viscous gas. Namely, a crossover in the temperature evolution when at least one of the samples presents non-monotonic relaxation. The influence of the bath on the dynamics of the particles is modeled via a viscous drag force plus a stochastic Langevin-like term. Each component of the mixture interchanges energy with the bath depending on the mechanical properties of its particles. This discrimination causes the coupling between the time evolution of temperature with that of the partial temperatures of each component. The non-monotonic Mpemba effect—and its inverse and mixed counterparts—stems from this coupling. In order to obtain analytical results, the velocity distribution functions of each component are approximated by considering multitemperature Maxwellian distributions. The theoretical results derived from the Enskog kinetic theory show an excellent agreement with direct simulation Monte Carlo (DMSC) data.

Phenomenology of vector-like leptons with Deep Learning at the Large Hadron Collider

In this paper, a model inspired by Grand Unification principles featuring three generations of vector-like fermions, new Higgs doublets and a rich neutrino sector at the low scale is presented. Using the state-of-the-art Deep Learning techniques we perform the first phenomenological analysis of this model focusing on the study of new charged vector-like leptons (VLLs) and their possible signatures at CERN’s Large Hadron Collider (LHC). In our numerical analysis we consider signal events for vector-boson fusion and VLL pair production topologies, both involving a final state containing a pair of charged leptons of different flavor and two sterile neutrinos that provide a missing energy. We also consider the case of VLL single production where, in addition to a pair of sterile neutrinos, the final state contains only one charged lepton. We propose a novel method to identify missing transverse energy vectors by comparing the detector response with Monte-Carlo simulated data. All calculated observables are provided as data sets for Deep Learning analysis, where a neural network is constructed, based on results obtained via an evolutive algorithm, whose objective is to maximise either the accuracy metric or the Asimov significance for different masses of the VLL. Taking into account the effect of the three analysed topologies, we have found that the combined significance for the observation of new VLLs at the high-luminosity LHC can range from 5.7σ, for a mass of 1.25 TeV, all the way up to 28σ if the VLL mass is 200 GeV. We have also shown that by the end of the LHC Run-III a 200 GeV VLL can be excluded with a confidence of 8.8 standard deviations. The results obtained show that our model can be probed well before the end of the LHC operations and, in particular, providing important phenomenological information to constrain the energy scale at which new gauge symmetries emergent from the considered Grand Unification picture can be manifest.

The Cherenkov Telescope Array production system proto-type for large-scale data processing and simulations

The Cherenkov Telescope Array (CTA) is the next-generation instrument in the very-high energy gamma ray astronomy domain. It will consist of tens of Cherenkov telescopes deployed in 2 arrays at La Palma (Spain) and Paranal (ESO, Chile) respectively. Currently under construction, CTA will start operations around 2023 for a duration of about 30 years. During operations CTA is expected to produce about 2 PB of raw data per year plus 5-20 PB of Monte Carlo data. The global data volume to be managed by the CTA archive, including all versions and copies, is of the order of 100 PB with a smooth growing profile. The associated processing needs are also very high, of the order of hundreds of millions of CPU HS06 hours per year. In order to optimize the instrument design and study its performances, during the preparatory phase (2010-2017) and the current construction phase, the CTA consortium has run massive Monte Carlo productions on the EGI grid infrastructure. In order to handle these productions and the future data processing, we have developed a production system based on the DIRAC framework. The current system is the result of several years of hardware infrastructure upgrades, software development and integration of different services like CVMFS and FTS. In this paper we present the current status of the CTA production system and its exploitation during the latest large-scale Monte Carlo campaigns.

Containerization in ATLAS Software Development and Data Production

The ATLAS experiment’s software production and distribution on the grid benefits from a semi-automated infrastructure that provides up-to-date information about software usability and availability through the CVMFS distribution service for all relevant systems. The software development process uses a Continuous Integration pipeline involving testing, validation, packaging and installation steps. For opportunistic sites that can not access CVMFS, containerized releases are needed. These standalone containers are currently created manually to support Monte-Carlo data production at such sites. In this paper we will describe an automated procedure for the containerization of ATLAS software releases in the existing software development infrastructure, its motivation, integration and testing in the distributed computing system.

Особенности вырождения основного состояния спин-псевдоспиновой модели двумерного магнетика вблизи точки фрустрации

The classical Monte Carlo method is used for the study of properties of the ground state and phase transitions of the spin-pseudospin model describing a two-dimensional Ising magnet with competing charge and spin interactions. This competition causes ground state degeneracy and frustration. It is shown that the ground state degeneracy is observed in the frustration area with nonzero probabilities of the formation of two different ordered states. Based on histogram analysis of Monte-Carlo data, the type of phase transitions is analyzed. It is found that first order phase transitions are observed near the frustration point, depending on the relationship between the spin s = 1/2 and pseudospin S = 1 interactions.

Accessing the ordered phase of correlated Fermi systems: Vertex bosonization and mean-field theory within the functional renormalization group

We present a consistent fusion of functional renormalization group and mean-field theory which explicitly introduces a bosonic field via a Hubbard-Stratonovich transformation at the critical scale, at which the order sets in. We show that a minimal truncation of the flow equations, that neglects order parameter fluctuations, is integrable and fulfills fundamental constraints as the Goldstone theorem and the Ward identity connected with the broken global symmetry. To introduce the bosonic field, we present a technique to factorize the most singular part of the vertex, even when the full dependence on all its arguments is retained. We test our method on the two-dimensional attractive Hubbard model at half-filling and calculate the superfluid gap as well as the Yukawa couplings and residual two fermion interactions in the ordered phase as functions of fermionic Matsubara frequencies. Furthermore, we analyze the gap and the condensate fraction for weak and moderate couplings and compare our results with previous functional renormalization group studies, and with quantum Monte Carlo data. Our formalism constitutes a convenient starting point for the inclusion of order parameter fluctuations by keeping a full, non simplified, dependence on fermionic momenta and/or frequencies.

Estimation of Unknown Parameters of Truncated Normal Distribution under Adaptive Progressive Type II Censoring Scheme

In reality, estimations for the unknown parameters of truncated distribution with censored data have wide utilization. Truncated normal distribution is more suitable to fit lifetime data compared with normal distribution. This article makes statistical inferences on estimating parameters under truncated normal distribution using adaptive progressive type II censored data. First, the estimates are calculated through exploiting maximum likelihood method. The observed and expected Fisher information matrices are derived to establish the asymptotic confidence intervals. Second, Bayesian estimations under three loss functions are also studied. The point estimates are calculated by Lindley approximation. Importance sampling technique is applied to discuss the Bayes estimates and build the associated highest posterior density credible intervals. Bootstrap confidence intervals are constructed for the purpose of comparison. Monte Carlo simulations and data analysis are employed to present the performances of various methods. Finally, we obtain optimal censoring schemes under different criteria.

Comprehensive characterization of ExacTrac stereoscopic image guidance system using Monte Carlo and Spektr simulations

The purpose of this work is to develop accurate computational methods to comprehensively characterize and model the clinical ExacTrac imaging system, which is used as an image guidance system for stereotactic treatment applications.The Spektr toolkit was utilized to simulate the spectral and imaging characterization of the system. Since Spektr only simulates the primary beam (ignoring scatter), a full model of ExacTrac was also developed in Monte Carlo (MC) to characterize the imaging system. To ensure proper performance of both simulation models, Spektr and MC data were compared to the measured spectral and half value layers (HVLs) values.To validate the simulation results, x-ray spectra of the ExacTrac system were measured for various tube potentials using a CdTe spectrometer with multiple added narrow collimators. The raw spectra were calibrated using a 57Co source and corrected for the escape peaks and detector efficiency. HVLs in mm of Al for various energies were measured using a calibrated RaySafe detector. Spektr and MC HVLs were calculated and compared to the measured values. The patient surface dose was calculated for different clinical imaging protocols from the measured air kerma and HVL values following the TG-61 methodology. The x-ray focal spot was measured by slanted edge technique using gafchromic films. ExacTrac imaging system beam profiles were simulated for various energies by MC simulation and the results were benchmarked by experimentally acquired beam profiles using gafchromic films. The effect of 6D IGRT treatment couch on beam hardening, dynamic range of the flat panel detector and scatter effect were determined using both Spektr simulation and experimental measurements.The measured and simulated spectra (of both MC and Spektr) for various kVps were compared and agreed within acceptable error. As another validation, the measured HVLs agreed with the Spektr and MC simulated HVLs on average within 1.0% for all kVps. The maximum and minimum patient surface doses were found to be 1.06 mGy for shoulder (high) and 0.051 mGy for cranial (low) imaging protocols, respectively. The MC simulated beam profiles were well matched with experimental results and replicated the penumbral slopes, the heel effect, and out-of-field regions. Dynamic range of detector (in terms of air kerma at detector surface) was found to be in the range of [6.1 × 10−6, 5.3 × 10−3] mGy.Accurate MC and Spektr models of the ExacTrac image guidance system were successfully developed and benchmarked via experimental validation. While patient surface dose for available imaging protocols were reported in this study, the established MC model may be used to obtain 3D imaging dose distribution for real patient geometries.

Finite-size effects in the reconstruction of dynamic properties from ab initio path integral Monte Carlo simulations.

We systematically investigate finite-size effects in the dynamic structure factor S(q,ω) of the uniform electron gas obtained via the analytic continuation of ab initio path integral Monte Carlo data for the imaginary-time density-density correlation function F(q,τ). Using the recent scheme by Dornheim etal. [Phys. Rev. Lett. 121, 255001 (2018)PRLTAO0031-900710.1103/PhysRevLett.121.255001], we find that the reconstructed spectra are not afflicted with any finite-size effects for as few as N=14 electrons both at warm dense matter (WDM) conditions and at the margins of the strongly correlated electron liquid regime. Our results further corroborate the high quality of our current description of the dynamic density response of correlated electrons, which is of high importance for many applications in WDM theory and beyond.

Boltzmann-based second-order constitutive models of diatomic and polyatomic gases including the vibrational mode

Describing diatomic and polyatomic gases at high temperatures requires a deep understanding of the excitation of molecules to a higher vibrational level. We developed new second-order constitutive models for diatomic and polyatomic gases with vibrational degrees of freedom, starting from the modified Boltzmann–Curtiss kinetic equation. The closing-last balanced closure and cumulant expansion of the calortropy production associated with the Boltzmann collision term are key to the derivation of the second-order models, compatible with the second law of thermodynamics. The topology of the constitutive models showed the presence of highly nonlinear and coupled protruding or sunken regions in the compression branch. It was also shown that the vibrational mode reduces the level of nonlinearity in the topology. In addition, analysis of a strong shock structure highlighted the interplay between the second-order effects in the constitutive relations and the vibrational–translational relaxation. Finally, the analysis showed that the results of the second-order models were in better agreement with the direct simulation Monte Carlo data, when compared with the results of the first-order models, especially in the profiles and slopes of density, velocity, and vibrational temperatures.

Effective Static Approximation: A Fast and Reliable Tool for Warm-Dense Matter Theory.

We present an effective static approximation (ESA) to the local field correction (LFC) of the electron gas that enables highly accurate calculations of electronic properties like the dynamic structure factor S(q,ω), the static structure factor S(q), and the interaction energy v. The ESA combines the recent neural-net representation by T. Dornheim et al., [J. Chem. Phys. 151, 194104 (2019)JCPSA60021-960610.1063/1.5123013] of the temperature-dependent LFC in the exact static limit with a consistent large wave-number limit obtained from quantum MonteCarlo data of the on-top pair distribution function g(0). It is suited for a straightforward integration into existing codes. We demonstrate the importance of the LFC for practical applications by reevaluating the results of the recent x-ray Thomson scattering experiment on aluminum by Sperling etal. [Phys. Rev. Lett. 115, 115001 (2015)PRLTAO0031-900710.1103/PhysRevLett.115.115001]. We find that an accurate incorporation of electronic correlations in terms of the ESA leads to a different prediction of the inelastic scattering spectrum than obtained from state-of-the-art models like the Mermin approach or linear-response time-dependent density functional theory. Furthermore, the ESA scheme is particularly relevant for the development of advanced exchange-correlation functionals in density functional theory.

On calculation of the average linear energy transfer for radiobiological modelling

Applying the concept of linear energy transfer (LET) to modelling of biological effects of charged particles usually involves calculation of the average LET. To calculate this, the energy distribution of particles is characterized by either the source spectrum or fluence spectrum. Also, the average can be frequency- or dose-weighted. This makes four methods of calculating the average LET, each producing a different number. The purpose of this note is to describe which of these four methods is best suited for radiobiological modelling. We focused on data for photons (x-rays and gamma radiation) because in this case differences in the four averaging methods are most pronounced. However, our conclusions are equally applicable to photons and hadrons. We based our arguments on recently emerged Monte Carlo data that fully account for transport of electrons down to very low energies comparable to the ionization potential of water. We concluded that the frequency average LET calculated using the fluence spectrum has better predictive power than does that calculated using any of the other three options. This optimal method is not new but is different from those currently dominating research in this area.

Asymptotic correlation functions in the Q-state Potts model: A universal form for point group C_{4v}.

Reexamining algebraic curves found in the eight-vertex model, we propose an asymptotic form of the correlation functions for off-critical systems possessing rotational and mirror symmetries of the square lattice, i.e., the C_{4v} symmetry. In comparison with the use of the Ornstein-Zernike form, it is efficient to investigate the correlation length with its directional dependence (or anisotropy). We investigate the Q-state Potts model on the square lattice. Monte Carlo (MC) simulations are performed using the infinite-size algorithm by Evertz and von der Linden. Fitting the MC data with the asymptotic form above the critical temperature, we reproduce the exact solution of the the anisotropic correlation length (ACL) of the Ising model (Q=2) within a five-digit accuracy. For Q=3 and 4, we obtain numerical evidence that the asymptotic form is applicable to their correlation functions and the ACLs. Furthermore, we successfully apply it to the bond percolation problem which corresponds to the Q→1 limit. From the calculated ACLs, the equilibrium crystal shapes (ECSs) are derived via duality and Wulff's construction. Regarding Q as a continuous variable, we find that the ECS of the Q-state Potts model is essentially the same as those of the Ising models on the Union Jack and 4-8 lattices, which are represented in terms of a simple algebraic curve of genus 1.

Dual fermion method as a prototype of generic reference-system approach for correlated fermions

We present a purely diagrammatic derivation of the dual fermion scheme (Rubtsov et al., 2008). The derivation makes particularly clear that a similar scheme can be developed for an arbitrary reference system provided it has the same interaction term as the original system. Thereby no restrictions are imposed by the locality of the reference problem or by the nature of the original problem as a lattice one. We present new arguments in favour of keeping the dual denominator in the expression for the lattice self-energy independently of the truncation of the dual interaction. As an example we present the computational results for the half-filled 2D Hubbard model with the choice of a 2 × 2 plaquette with periodic boundary conditions as a reference system. We observe that obtained results are in a good agreement with numerically exact lattice quantum Monte Carlo data.