Massively Multidimensional Diffusion-Relaxation Correlation MRI

Diverse approaches such as oscillating gradients, tensor-valued encoding, and diffusion-relaxation correlation have been used to study microstructure and heterogeneity in healthy and pathological biological tissues. Recently, acquisition schemes with free gradient waveforms exploring both the frequency-dependent and tensorial aspects of the encoding spectrum b(ω) have enabled estimation of nonparametric distributions of frequency-dependent diffusion tensors. These “D(ω)-distributions” allow investigation of restricted diffusion for each distinct component resolved in the diffusion tensor trace, anisotropy, and orientation dimensions. Likewise, multidimensional methods combining longitudinal and transverse relaxation rates, R1 and R2, with (ω-independent) D-distributions capitalize on the component resolution offered by the diffusion dimensions to investigate subtle differences in relaxation properties of sub-voxel water populations in the living human brain, for instance nerve fiber bundles with different orientations. By measurements on an ex vivo rat brain, we here demonstrate a “massively multidimensional” diffusion-relaxation correlation protocol joining all the approaches mentioned above. Images acquired as a function of the magnitude, normalized anisotropy, orientation, and frequency content of b(ω), as well as the repetition time and echo time, yield nonparametric D(ω)-R1-R2-distributions via a Monte Carlo data inversion algorithm. The obtained per-voxel distributions are converted to parameter maps commonly associated with conventional lower-dimensional methods as well as unique statistical descriptors reporting on the correlations between restriction, anisotropy, and relaxation.

Many-body and temperature effects in two-dimensional quantum droplets in Bose–Bose mixtures

We study the equilibrium properties of self-bound droplets in two-dimensional Bose mixtures employing the time-dependent Hartree–Fock–Bogoliubov theory. This theory allows one to understand both the many-body and temperature effects beyond the Lee–Huang–Yang description. We calculate higher-order corrections to the excitations, the sound velocity, and the energy of the droplet. Our results for the ground-state energy are compared with the diffusion Monte Carlo data and good agreement is found. The behavior of the depletion and anomalous density of the droplet is also discussed. At finite temperature, we show that the droplet emerges at temperatures well below the Berezinskii–Kosterlitz–Thouless transition temperature. The critical temperature strongly depends on the interspecies interactions. Our study is extended to the finite size droplet by numerically solving the generalized finite-temperature Gross-Pitaevskii equation which is obtained self-consistently from our formalism in the framework of the local density approximation.

Impact of background effects on the inclusive Vcb determination

The determination of the CKM element Vcb from inclusive semileptonic b → cℓ$$ \overline{\nu} $$ ν ¯ decays has reached a high precision thanks to a combination of theoretical and experimental efforts. Aiming towards even higher precision, we discuss two processes that contaminate the inclusive Vcb determination; the b → u background and the contribution of the tauonic mode: b → c(τ → μν$$ \overline{\nu} $$ ν ¯ )$$ \overline{\nu} $$ ν ¯ . Both of these contributions are dealt with at the experimental side, using Monte-Carlo methods and momentum cuts. However, these contributions can be calculated with high precision within the Heavy-Quark Expansion. In this note, we calculate the theoretical predictions for these two processes. We compare our b → u results qualitatively with generator-level Monte-Carlo data used at Belle and Belle II. Finally, we suggest to change the strategy for the extraction of Vcb by comparing the data on B → Xℓ directly with the theoretical expressions, to which our paper facilitates.

Low-temperature thermodynamic properties of the Heisenberg antiferromagnetic chain with two easy-axis single-ion anisotropies

In this paper, the spin wave theory is applied to the one-dimensional Heisenberg antiferromagnet in the coexistence of two different anisotropies [Formula: see text] and [Formula: see text], which are separately the easy-axis single-ion anisotropies for sublattice [Formula: see text] and sublattice [Formula: see text] of the system. Both the ground-state and low-temperature properties of the system are strongly affected by the competition between these two anisotropies. Two kinds of the competition in terms of the deviation parameter [Formula: see text] are discussed for the uniform anisotropy taking the values of [Formula: see text] and [Formula: see text], respectively. The [Formula: see text]-dependent behaviors (such as the power, exponential and linear laws) are obtained for the total magnetization, the staggered magnetizations, the internal energy, the specific heat and the susceptibility. It is found that at zero-temperature, the interplay between these two anisotropies induces the antiferromagnetic-disorder phase transition in the small anisotropy region with [Formula: see text]. For the selected cases of [Formula: see text], our results for are in agreement with the findings obtained by the existing theories and the quantum Monte Carlo data.

Pengukuran Conditional Value At Risk (CVAR) Pada Aset Tunggal dengan Metode Simulasi Monte Carlo

Conditional value at risk (CVaR) merupakan suatu ukuran risiko yang memperhitungkan kerugian melebihi tingkat Value at risk (VaR). Tujuan dalam penelitian ini adalah mendapatkan hasil pengukuran Conditional Value at Risk (CVaR) pada aset tunggal dengan menggunakan metode simulasi Monte Carlo. Data yang digunakan dalam penelitian ini ialah harga penutupan saham harian PT. Bank Central Asia Tbk (BBCA.JK) dengan tingkat kepercayaan . Dari hasil perhitungan CVaR pada tingkat kepercayaan 99%, menghasilkan nilai CVaR sebesar . Hal ini dapat diartikan bahwa ada keyakinan sebesar kerugian yang mungkin akan diderita investor tidak akan melebihi dalam jangka waktu satu hari setelah tanggal 30 September 2020, atau dengan kata lain ada kemungkinan sebesar bahwa kerugian investasi pada periode tersebut sebesar atau lebih dalam jangka waktu satu hari dengan dana awal yang diinvestasikan sebesar Rp

Biomass Hydrothermal Carbonization: Markov-Chain Monte Carlo Data Analysis and Modeling

This paper introduces Bayesian statistical methods for studying the kinetics of biomass hydrothermal carbonization. Two simple, specially developed computer programs implement Markov-chain Monte Carlo methods to illustrate these techniques' potential, long since established in other areas of chemical reaction engineering. A range of experimental data, both from this study and the literature, test the soundness of a Bayesian approach to modeling biomass hydrothermal carbonization kinetics. The first program carries out parameter estimations and performs better or equal than the traditional deterministic methods (R2 as high as 0.9998). For three out of the 22 datasets, the program detected the global minima of the parameter space, while the deterministic least-square found local values. The second program uses Gillespie's algorithm for the statistical simulation of the reactions occurring in hydrothermal carbonization. Comparing six basic kinetic models with literature data tested the stochastic simulation as a tool for assessing biomass conversion reaction networks rapidly. Among the simple models discussed, reaction scheme 3 fitted better to the experimental data (R2 > 0.999). The proposed approach is worth extending to more complex, time-consuming computer models and could support other techniques for studying hydrothermal conversions.

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.

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.