Uncorrelated Sampling Research Articles

Integrated reconstructive spectrometer with programmable photonic circuits

Optical spectroscopic sensors are a powerful tool to reveal light-matter interactions in many fields. Miniaturizing the currently bulky spectrometers has become imperative for the wide range of applications that demand in situ or even in vitro characterization systems, a field that is growing rapidly. In this paper, we propose a novel integrated reconstructive spectrometer with programmable photonic circuits by simply using a few engineered MZI elements. This design effectively creates an exponentially scalable number of uncorrelated sampling channels over an ultra-broad bandwidth without incurring additional hardware costs, enabling ultra-high resolution down to single-digit picometers. Experimentally, we implement an on-chip spectrometer with a 6-stage cascaded MZI structure and demonstrate <10 pm resolution with >200 nm bandwidth using only 729 sampling channels. This achieves a bandwidth-to-resolution ratio of over 20,000, which is, to our best knowledge, about one order of magnitude greater than any reported miniaturized spectrometers to date.

Multiscale modeling of linear elastic heterogeneous structures via localized model order reduction

AbstractIn this article, a methodology for fine scale modeling of large scale linear elastic structures is proposed, which combines the variational multiscale method, domain decomposition and model order reduction. The influence of the fine scale on the coarse scale is modeled by the use of an additive split of the displacement field, addressing applications without a clear scale separation. Local reduced spaces are constructed by solving an oversampling problem with random boundary conditions. Herein, we inform the boundary conditions by a global reduced problem and compare our approach using physically meaningful correlated samples with existing approaches using uncorrelated samples. The local spaces are designed such that the local contribution of each subdomain can be coupled in a conforming way, which also preserves the sparsity pattern of standard finite element assembly procedures. Several numerical experiments show the accuracy and efficiency of the method, as well as its potential to reduce the size of the local spaces and the number of training samples compared to the uncorrelated sampling.

Autoregressive neural Slater-Jastrow ansatz for variational Monte Carlo simulation

Direct sampling from a Slater determinant is combined with an autoregressive deep neural network as a Jastrow factor into a fully autoregressive Slater-Jastrow ansatz for variational quantum Monte Carlo, which allows for uncorrelated sampling. The elimination of the autocorrelation time leads to a stochastic algorithm with provable cubic scaling (with a potentially large prefactor), i.e. the number of operations for producing an uncorrelated sample and for calculating the local energy scales like \mathcal{O}(N_s^3)𝒪(Ns3) with the number of orbitals N_sNs. The implementation is benchmarked on the two-dimensional t-Vt−V model of spinless fermions on the square lattice.

Multiscale statistical quantum transport in porous media and random alloys with vacancies

We have developed a multiscale self-consistent method to study the charge conductivity of a porous system or a metallic matrix alloyed by randomly distributed nonmetallic grains and vacancies by incorporating Schrödinger’s equation and Poisson’s equation. To account for the random distribution of the nonmetallic grains and clusters within the alloy system, we have used an uncorrelated white-noise Monte Carlo sampling to generate numerous random alloys and statistically evaluate the charge conductance. We have performed a parametric study and investigated various electrical aspects of random porous and alloy systems as a function of the inherent parameters and density of the random grains. Our results find that the charge conductance within the low-voltage regime shows a highly nonlinear behavior against voltage variations in stark contrast to the high-voltage regime where the charge conductance is constant. The former finding is a direct consequence of the quantum scattering processes. The results reveal the threshold to the experimentally observable quantities, e.g., voltage difference, so that the charge current is activated for values larger than the threshold. The numerical study determines the threshold of one quantity as a function of the remaining quantities. Our method and results can serve to guide future experiments in designing circuital elements, involving this type of random alloy system.

Analytical solutions in amplitude and time measurements from discrete sampling of pseudo-Gaussian signals

Analytical solutions for amplitude and time measurements from digitized signals of the pseudo-Gaussian shape are considered. The least squares method (l.s.m.) is chosen as the algorithm to determine amplitude A and timestamp t0. For a profile with an uncorrelated sampling the l.s.m. is reduced to analytical formulas consistent with the experiment. This permits to estimate the desired number of points Ns on a profile. The obtained results for Ns are illustrated with qualitative estimates in accordance with the Nyquist–Shannon–Kotelnikov sampling theorem. The optimality of the electronic filters forming the waveform is analyzed in terms of the excess noise factor. An analytical solution is found for the autocorrelation function from stochastic noise sources. It permits to define non-diagonal weight matrix elements in the l.s.m. with formulation of requirements for neglecting sampling correlations.

GROMACS implementation of free energy calculations with non-pairwise Variationally derived Intermediates

Gradients in free energies are the driving forces of physical and biochemical systems. To predict free energy differences with high accuracy, Molecular Dynamics (MD) and other methods based on atomistic Hamiltonians conduct sampling simulations in intermediate thermodynamic states that bridge the configuration space densities between two states of interest (’alchemical transformations’). For uncorrelated sampling, the recent Variationally derived Intermediates (VI) method yields optimal accuracy. The form of the VI intermediates differs fundamentally from conventional ones in that they are non-pairwise, i.e., the total force on a particle in an intermediate states cannot be split into additive contributions from the surrounding particles. In this work, we describe the implementation of VI into the widely used GROMACS MD software package (2020, version 1). Furthermore, a variant of VI is developed that avoids numerical instabilities for vanishing particles. The implementation allows the use of previous non-pairwise potential forms in the literature, which have so far not been available in GROMACS. Example cases on the calculation of solvation free energies, and accuracy assessments thereof, are provided. Program summaryProgram Title: GROMACS-VI-ExtensionCPC Library link to program files:https://doi.org/10.17632/7yvc8mmnyv.1Developer’s repository link:https://www.mpibpc.mpg.de/gromacs-vi-extension and https://www.gitlab.gwdg.de/martin.reinhardt/gromacs-vi-extensionLicensing provisions: LGPLProgramming language: C++14, CUDANature of problem: The free energy difference between two states of a thermodynamic system is calculated using samples generated by simulations based on atomistic Hamiltonians. Due to the high dimensionality of many applications as in, e.g., biophysics, only a small part of the configuration space can be sampled. The choice of the sampling scheme critically affects the accuracy of the final free energy estimate. The challenge is, therefore, to find the optimal sampling scheme that provides best accuracy for given computational effort.Solution method: Sampling is commonly conducted in intermediate states, whose Hamiltonians are defined based on the Hamiltonians of the two states of interest. Here, sampling is conducted in the variationally derived intermediate states that, under the assumption of uncorrelated sample points, yield optimal accuracy. These intermediates differ fundamentally from the common intermediates in that they are non-pairwise, i.e., the forces on a particle are only additive in the end state, whereas the total force in the intermediate states cannot be split into additive contributions from the surrounding particles.

The Variationally Derived Intermediates Method to Calculate Free Energy Differences

Accurate and fast free energy calculations, based on atomistic simulations, are key to a first principles understanding of many-particle systems in biophysics, and enable quantitative descriptions of molecular recognition processes, drug binding, transmembrane transport, or functional conformational motions of proteins or complexes. To this aim, alchemical methods, such as the Free Energy Perturbation or the Bennett Acceptance Ratio method, require ‘morphing’ between the Hamiltonians of the involved molecular end states, typically in terms of a linear interpolation. However, linear transformations and soft-core variants thereof are still a very special case amongst all possible transformations. Here, we present the Variationally Derived Intermediates (VI) method that generalizes this approach and yields, under the assumption of uncorrelated sampling points, the intermediates with optimal sampling accuracy, which differ markedly from the established ones. We present applications to the challenging case of solvation free energies, yielding improved accuracies for decoupling electrostatic interactions, and similar ones for Lennard-Jones interactions, compared to state of the art soft-core transformations.

Fully on-chip clock jitter and skew measurement scheme via incoherent subsampling

An incoherent subsampling scheme for on-chip measurement of high-speed clock jitter and skew is presented. A simple inverter-based ring oscillator with frequency selection multiplexers is used to generate uniform and uncorrelated sampling events when binned in the unit period of the clock. The measurement results are directly reflected in the on-chip counters which are proportional to the injected jitter and skew. The measurement errors can be reduced with increasing sampling numbers. Theories of ring oscillator period suitability, sampling number requirement and jitter measurement are analyzed in detail. Behavioral simulations using MATLAB are performed to verify the proposed theories. The measurement circuit is implemented using a 55 ​nm CMOS process and the maximum measurement errors in skew mode and jitter mode from SPICE simulations are 0.121ps and 0.123 ​ps, respectively. The implemented measurement circuit has good immunity to PVT variations after proper tuning and the influence of supply noise is also investigated.

Hyperspatial optimization of structures

Anticipating the low energy arrangements of atoms in space is an indispensable scientific task. Modern stochastic approaches to searching for these configurations depend on the optimisation of structures to nearby local minima in the energy landscape. In many cases these local minima are relatively high in energy, and inspection reveals that they are trapped, tangled, or otherwise frustrated in their descent to a lower energy configuration. Strategies have been developed which attempt to overcome these traps, such as classical and quantum annealing, basin/minima hopping, evolutionary algorithms and swarm based methods. Random structure search makes no attempt to avoid the local minima, and benefits from a broad and uncorrelated sampling of configuration space. It has been particularly successful in the first principles prediction of unexpected new phases of dense matter. Here it is demonstrated that by starting the structural optimisations in a higher dimensional space, or hyperspace, many of the traps can be avoided, and that the probability of reaching low energy configurations is much enhanced. Excursions into the extra dimensions are progressively eliminated through the application of a growing energetic penalty. This approach is tested on hard cases for random search - clusters, compounds, and covalently bonded networks. The improvements observed are most dramatic for the most difficult ones. Random structure search is shown to be typically accelerated by two orders of magnitude, and more for particularly challenging systems. This increase in performance is expected to benefit all approaches to structure prediction that rely on the local optimisation of stochastically generated structures.

Prospects for future satellite estimation of small-scale variability of ocean surface velocity and vorticity

Prospects for future satellite estimation of small-scale variability of ocean surface velocity and vorticity

CMOS Image Sensor Random Telegraph Noise Time Constant Extraction From Correlated To Uncorrelated Double Sampling

A new method for on-chip random telegraph noise (RTN) characteristic time constant extraction using the double sampling circuit in an 8.3 Mpixel CMOS image sensor is described. The dependence of the measured RTN on the time difference between the double sampling and the key equation used for time constant extraction are derived from the continuous time RTN model and the discrete event RTN model. Both approaches lead to the same result and describe the data reasonably well. From the detailed study of the noisiest 1000 pixels, we find that about 75% to 85% of them show the signature of a single-trap RTN behavior with three distinct signal levels, and about 96% of the characteristic time constants fall between 1 ${\mathrm{ \mu }}\text{s}$ and 500 ${\mathrm{ \mu }}\text{s}$ with the median around 10 ${\mathrm{ \mu }}\text{s}$ at room temperature.

An efficient algorithm to perform local concerted movements of a chain molecule.

The devising of efficient concerted rotation moves that modify only selected local portions of chain molecules is a long studied problem. Possible applications range from speeding the uncorrelated sampling of polymeric dense systems to loop reconstruction and structure refinement in protein modeling. Here, we propose and validate, on a few pedagogical examples, a novel numerical strategy that generalizes the notion of concerted rotation. The usage of the Denavit-Hartenberg parameters for chain description allows all possible choices for the subset of degrees of freedom to be modified in the move. They can be arbitrarily distributed along the chain and can be distanced between consecutive monomers as well. The efficiency of the methodology capitalizes on the inherent geometrical structure of the manifold defined by all chain configurations compatible with the fixed degrees of freedom. The chain portion to be moved is first opened along a direction chosen in the tangent space to the manifold, and then closed in the orthogonal space. As a consequence, in Monte Carlo simulations detailed balance is easily enforced without the need of using Jacobian reweighting. Moreover, the relative fluctuations of the degrees of freedom involved in the move can be easily tuned. We show different applications: the manifold of possible configurations is explored in a very efficient way for a protein fragment and for a cyclic molecule; the “local backbone volume”, related to the volume spanned by the manifold, reproduces the mobility profile of all-α helical proteins; the refinement of small protein fragments with different secondary structures is addressed. The presented results suggest our methodology as a valuable exploration and sampling tool in the context of bio-molecular simulations.

Statistically optimal analysis of state-discretized trajectory data from multiple thermodynamic states.

We propose a discrete transition-based reweighting analysis method (dTRAM) for analyzing configuration-space-discretized simulation trajectories produced at different thermodynamic states (temperatures, Hamiltonians, etc.) dTRAM provides maximum-likelihood estimates of stationary quantities (probabilities, free energies, expectation values) at any thermodynamic state. In contrast to the weighted histogram analysis method (WHAM), dTRAM does not require data to be sampled from global equilibrium, and can thus produce superior estimates for enhanced sampling data such as parallel/simulated tempering, replica exchange, umbrella sampling, or metadynamics. In addition, dTRAM provides optimal estimates of Markov state models (MSMs) from the discretized state-space trajectories at all thermodynamic states. Under suitable conditions, these MSMs can be used to calculate kinetic quantities (e.g., rates, timescales). In the limit of a single thermodynamic state, dTRAM estimates a maximum likelihood reversible MSM, while in the limit of uncorrelated sampling data, dTRAM is identical to WHAM. dTRAM is thus a generalization to both estimators.

Role of sampling in evaluating classical time autocorrelation functions

We analyze how the choice of the sampling weight affects efficiency of the Monte Carlo evaluation of classical time autocorrelation functions. Assuming uncorrelated sampling or sampling with constant correlation length, we propose a sampling weight for which the number of trajectories needed for convergence is independent of the correlated quantity, dimensionality, dynamics, and phase-space density. By contrast, it is shown that the computational cost of the "standard" algorithm sampling from the phase-space density may scale exponentially with the number of degrees of freedom. Yet, for the stationary Gaussian distribution of harmonic systems and for the autocorrelation function of a linear function of phase-space coordinates, the computational cost of this standard algorithm is also independent of dimensionality.

On using correlated sampling to simulate small changes in system response by MCNP

Correlated sampling is a developed technique that enables MCNP to simulate small changes in system response with an acceptable uncertainty at reasonable number of particle histories. In this work the performance of correlated sampling is investigated. It is found that under certain conditions using the default output format of MCNP and the original practice of batch statistics developed for correlated sampling may overestimate the uncertainty of a response change. The cause of the overestimation is analyzed; correspondingly two suggestions are proposed for correlated sampling to ensure correct estimation of the uncertainty. The performance of improved correlated sampling is compared with that of un-correlated sampling computation to demonstrate the effect of correlated sampling. Results show that correlated sampling indeed is a robust technique for MCNP to simulate small changes in system response.

The matrix- t distribution and its applications in predictive inference

The predictive distributions of the future responses and regression matrix under the multivariate elliptically contoured distributions are derived using structural approach. The predictive distributions are obtained as matrix- t which are identical to those obtained under matrix normal and matrix- t distributions. This gives inference robustness with respect to departures from the reference case of independent sampling from the matrix normal or dependent but uncorrelated sampling from matrix- t distributions. Some successful applications of matrix- t distribution in the field of spatial prediction have been addressed.

Linkage disequilibrium in two‐stage marker‐assisted selection

Linkage disequilibrium in two‐stage marker‐assisted selection

Optimal effort allocation in stratified, large area trawl surveys, with application to shrimp surveys in the Barents Sea

A method for optimal effort allocation in stratified trawl surveys with uncorrelated grid sampling is developed. Two related optimisation criteria are considered: (1) to minimise the coefficient of variation (CV) of the biomass index for a given available vessel time ( t) and (2) to minimise the vessel time needed in order to obtain a required CV value. The cost function model includes a constant trawl and handling time per station, and a stratum-dependent sailing time between successive stations. The benefit of the method is compared with a conventional design with proportional (to area) allocation. Simple formulas for reasonably close upper and lower bounds for the obtainable improvement are calculated. In general, the maximum relative reduction in t for a given CV value is larger than the obtainable relative reduction in CV for a given t. Applied to biomass data from conventional shrimp surveys in the Barents Sea (1992–1996), it is estimated that the mean CV value (averaged over years) could have been reduced from 7.0% (proportional allocation) to 6.4% (optimal allocation), which corresponds to a relative reduction of 8.7%. Correspondingly, a possible 10.9% reduction of t was found without loss of precision.