Arbitrary Truncation Research Articles

Toward QCD on quantum computer: orbifold lattice approach

We propose an orbifold lattice formulation of QCD suitable for quantum simulations. We show explicitly how to encode gauge degrees of freedom into qubits using noncompact variables, and how to write down a simple truncated Hamiltonian in the coordinate basis. We show that SU(3) gauge group variables and quarks in the fundamental representation can be implemented straightforwardly on qubits, for arbitrary truncation of the gauge manifold.

Development of an analytical model for the flexural vibration of fish bone active camber structures with truncated, variable thickness partitions

The need for smooth, gapless mechanisms that offer superior aerodynamic performance has been the prime mover for a wide range of studies on the morphing concepts from the early years of the twenty-first century. In light of the importance of novel analytic means for inspecting such structures, this article describes a comprehensive dynamic model for the flexural vibration of a special type of morphing structure known as fish bone active camber (FishBAC). In view of the shortcomings of previous models, the developed procedure considers the variable thickness of the central spine of FishBAC as well as the possibility of arbitrary truncations in its numerous partitions to offer more accurate results. A general idea is first proposed based on the assumptions of classical plate theory for such partitioned structures. The equations are derived using the energy method and the assumption of artificial springs to satisfy the continuity of shear force and bending moment along the connecting lines between partitions. A robust Rayleigh-Ritz method along with a set of fast-converging admissible functions is presented to solve the governing equations of motion. Combined with the power of Mathematica and validated by other analytic models and finite element codes, this technique can be used to deal with a plethora of similar systems while paving the path for the dynamic analysis of FishBAC built around various airfoils.

Resolving ambiguities of the mode truncation in cavity quantum electrodynamics

This work provides the fundamental theoretical framework for few-mode cavity quantum electrodynamics by resolving the gauge ambiguities between the Coulomb gauge and the dipole gauge Hamiltonians under the photonic mode truncation. We first propose a general framework to resolve ambiguities for an arbitrary truncation in a given gauge. Then, we specifically consider the case of mode truncation, deriving gauge invariant expressions for both the Coulomb and dipole gauge Hamiltonians that naturally reduce to the commonly used single-mode Hamiltonians when considering a single-mode truncation. We finally provide the analytical and numerical results of both atomic and molecular model systems coupled to the cavity to demonstrate the validity of our theory.

Prospects for simulating a qudit-based model of (1+1)D scalar QED

We present a gauge invariant digitization of $(1+1)$d scalar quantum electrodynamics for an arbitrary spin truncation for qudit-based quantum computers. We provide a construction of the Trotter operator in terms of a universal qudit-gate set. The cost savings of using a qutrit based spin-1 encoding versus a qubit encoding are illustrated. We show that a simple initial state could be simulated on current qutrit based hardware using noisy simulations for two different native gate set.

Moments Calculation for the Doubly Truncated Multivariate Normal Density

In the present article, we derive an explicit expression for the truncated mean and variance for the multivariate normal distribution with arbitrary rectangular double truncation. We use the moment generating approach of Tallis (1961) and extend it to general μ, Σ and all combinations of truncation. As part of the solution, we also give a formula for the bivariate marginal density of truncated multinormal variates. We also prove an invariance property of some elements of the inverse covariance after truncation. Computer algorithms for computing the truncated mean, variance and the bivariate marginal probabilities for doubly truncated multivariate normal variates have been written in R and are presented along with three examples.

Comment on “Aharonov-Bohm effect for bound states from the interaction of the magnetic quadrupole moment of a neutral particle with axial fields”

We analyze recently published results about the Aharonov-Bohm effect for bound states from the interaction of the magnetic quadrupole moment of a neutral particle with axial fields. We show that the eigenvalues obtained by the authors from an arbitrary truncation of the Frobenius power series correspond to more than one model and, consequently, are unsuitable for drawing any sound physical conclusion. Besides, the prediction of allowed oscillator frequencies is a mere consequence of the truncation condition just mentioned.

Diagnosis of explicit symmetry breaking in the tight-binding constructions for symmetry-protected topological systems

It has been well established that for symmetry protected topological systems, the non-trivial topology prevents a real space representation using exponentially localized Wannier wavefunctions (WFs) in all directions, unless the protecting symmetry is sacrificed as an on-site transformation. This makes it challenging to determine the symmetry of various physical observables represented using such WFs. In this work, we propose a practical method for overcoming such challenges using the Kane-Mele model as a concrete example. We present a systematic procedure for diagnosing the symmetry of any observables, as well as a method for constructing symmetric operators up to arbitrary truncation accuracy.

Robust data-driven approach for predicting the configurational energy of high entropy alloys

High entropy alloys (HEAs) are promising next-generation materials due to their various excellent properties. To understand these properties, it's necessary to characterize the chemical ordering and identify order-disorder transitions through efficient simulation and modeling of thermodynamics. In this study, a robust data-driven framework based on Bayesian approaches is proposed for the accurate and efficient prediction of configurational energy of high entropy alloys. The recently proposed effective pair interaction (EPI) model with ensemble sampling is used to map the configuration and its corresponding energy. Given limited data calculated by first-principles calculations, Bayesian regularized regression not only offers an accurate and stable prediction but also effectively quantifies the uncertainties associated with EPI parameters. Compared with the arbitrary truncation of model complexity, we further conduct a physical feature selection to identify the truncation of coordination shells in EPI model using Bayesian information criterion. The results achieve efficient and robust performance in predicting the configurational energy, particularly given small data. The developed methodology is applied to study a series of refractory HEAs, i.e. NbMoTaW, NbMoTaWV and NbMoTaWTi where it is demonstrated how dataset size affects the confidence when data is sparse.

Large scale parallelization in stochastic coupled cluster.

Coupled cluster theory is a vital cornerstone of electronic structure theory and is being applied to ever-larger systems. Stochastic approaches to quantum chemistry have grown in importance and offer compelling advantages over traditional deterministic algorithms in terms of computational demands, theoretical flexibility, or lower scaling with system size. We present a highly parallelizable algorithm of the coupled cluster Monte Carlo method involving sampling of clusters of excitors over multiple time steps. The behavior of the algorithm is investigated on the uniform electron gas and the water dimer at coupled-cluster levels including up to quadruple excitations. We also describe two improvements to the original sampling algorithm, full non-composite, and multi-spawn sampling. A stochastic approach to coupled cluster results in an efficient and scalable implementation at arbitrary truncation levels in the coupled cluster expansion.

Filling the gaps: Gaussian mixture models from noisy, truncated or incomplete samples

Astronomical data often suffer from noise and incompleteness. We extend the common mixtures-of-Gaussians density estimation approach to account for situations with a known sample incompleteness by simultaneous imputation from the current model. The method, called GMMis, generalizes existing Expectation-Maximization techniques for truncated data to arbitrary truncation geometries and probabilistic rejection processes, as long as they can be specified and do not depend on the density itself. The method accounts for independent multivariate normal measurement errors for each of the observed samples and recovers an estimate of the error-free distribution from which both observed and unobserved samples are drawn. It can perform a separation of a mixtures-of-Gaussian signal from a specified background distribution whose amplitude may be unknown. We compare GMMis to the standard Gaussian mixture model for simple test cases with different types of incompleteness, and apply it to observational data from the NASA Chandra X-ray telescope. The python code is released as an open-source package at https://github.com/pmelchior/pyGMMis

Particle trajectories and mass transport under mechanically generated nonlinear water waves

A theoretical model is developed to study the kinematics of water particles and mass transport of wave-induced flow generated in a closed flume. A semi-analytical pseudo-spectral solution to the problem of mechanically generated nonlinear water waves propagating at a constant depth is derived under the potential flow assumptions. Velocity potential and free-surface displacement functions are represented in a form based on Fourier series. The eigenfunction expansions are resolved by means of a Fast Fourier Transform technique and a higher order time-stepping procedure. The derived nonlinear solution of the wavemaker problem is based on Taylor series representation of the free-surface and wavemaker boundary conditions expanded up to an arbitrary truncation order. This technique is employed to study the evolution of a velocity field and particle trajectories under regular gravity waves generated in a wave flume. The instantaneous velocity fields are integrated in time to calculate the particle trajectories and time-averaged spatial distribution of Lagrangian and Eulerian mean velocities. The theoretical results are compared with the available experimental data. A good agreement is observed, which confirms the applicability of the presented theory to the problems of transport processes associated with the propagation of water waves and their generation in the flume.

Better Than Nothing: A Rational Approach for Minimizing the Impact of Outflow Strategy on Cerebrovascular Simulations.

Computational fluid dynamics simulations of neurovascular diseases are impacted by various modeling assumptions and uncertainties, including outlet boundary conditions. Many studies of intracranial aneurysms, for example, assume zero pressure at all outlets, often the default ("do-nothing") strategy, with no physiological basis. Others divide outflow according to the outlet diameters cubed, nominally based on the more physiological Murray's law but still susceptible to subjective choices about the segmented model extent. Here we demonstrate the limitations and impact of these outflow strategies, against a novel "splitting" method introduced here. With our method, the segmented lumen is split into its constituent bifurcations, where flow divisions are estimated locally using a power law. Together these provide the global outflow rate boundary conditions. The impact of outflow strategy on flow rates was tested for 70 cases of MCA aneurysm with 0D simulations. The impact on hemodynamic indices used for rupture status assessment was tested for 10 cases with 3D simulations. Differences in flow rates among the various strategies were up to 70%, with a non-negligible impact on average and oscillatory wall shear stresses in some cases. Murray-law and splitting methods gave flow rates closest to physiological values reported in the literature; however, only the splitting method was insensitive to arbitrary truncation of the model extent. Cerebrovascular simulations can depend strongly on the outflow strategy. The default zero-pressure method should be avoided in favor of Murray-law or splitting methods, the latter being released as an open-source tool to encourage the standardization of outflow strategies.

Converging High-Level Coupled-Cluster Energetics by Monte Carlo Sampling and Moment Expansions

We propose a new approach to the determination of accurate electronic energies that are equivalent to the results of high-level coupled-cluster (CC) calculations. The approach is based on merging the CC(P;Q) formalism, which corrects energies obtained with an arbitrary truncation in the cluster operator, with the stochastic configuration interaction and CC ideas. The advantages of the proposed methodology are illustrated by molecular examples, where the goal is to recover the energetics obtained in the CC calculations with a full treatment of singly, doubly, and triply excited clusters.

Smooth semi-nonparametric (SNP) estimation of the cumulative incidence function.

This paper presents a novel approach to estimation of the cumulative incidence function in the presence of competing risks. The underlying statistical model is specified via a mixture factorization of the joint distribution of the event type and the time to the event. The time to event distributions conditional on the event type are modeled using smooth semi‐nonparametric densities. One strength of this approach is that it can handle arbitrary censoring and truncation while relying on mild parametric assumptions. A stepwise forward algorithm for model estimation and adaptive selection of smooth semi‐nonparametric polynomial degrees is presented, implemented in the statistical software R, evaluated in a sequence of simulation studies, and applied to data from a clinical trial in cryptococcal meningitis. The simulations demonstrate that the proposed method frequently outperforms both parametric and nonparametric alternatives. They also support the use of ‘ad hoc’ asymptotic inference to derive confidence intervals. An extension to regression modeling is also presented, and its potential and challenges are discussed. © 2017 The Authors. Statistics in Medicine Published by John Wiley & Sons Ltd.

Effective low-order models for atmospheric dynamics and time series analysis.

The paper focuses on two interrelated problems: developing physically sound low-order models (LOMs) for atmospheric dynamics and employing them as novel time-series models to overcome deficiencies in current atmospheric time series analysis. The first problem is warranted since arbitrary truncations in the Galerkin method (commonly used to derive LOMs) may result in LOMs that violate fundamental conservation properties of the original equations, causing unphysical behaviors such as unbounded solutions. In contrast, the LOMs we offer (G-models) are energy conserving, and some retain the Hamiltonian structure of the original equations. This work examines LOMs from recent publications to show that all of them that are physically sound can be converted to G-models, while those that cannot lack energy conservation. Further, motivated by recent progress in statistical properties of dynamical systems, we explore G-models for a new role of atmospheric time series models as their data generating mechanisms are well in line with atmospheric dynamics. Currently used time series models, however, do not specifically utilize the physics of the governing equations and involve strong statistical assumptions rarely met in real data.

Witt vector rings and the relative de Rham Witt complex

In this paper we develop a novel approach to Witt vector rings and to the (relative) de Rham Witt complex. We do this in the generality of arbitrary commutative algebras and arbitrary truncation sets. In our construction of Witt vector rings the ring structure is obvious and there is no need for universal polynomials. Moreover a natural generalization of the construction easily leads to the relative de Rham Witt complex. Our approach is based on the use of free or at least torsion free presentations of a given commutative ring R and it is an important fact that the resulting objects are independent of all choices. The approach via presentations also sheds new light on our previous description of the ring of p-typical Witt vectors of a perfect Fp-algebra as a completion of a semigroup algebra. We develop this description in different directions. For example, we show that the semigroup algebra can be replaced by any free presentation of R equipped with a linear lift of the Frobenius automorphism. Using the result in Appendix A by Umberto Zannier we also extend the description of the Witt vector ring as a completion to all F‾p-algebras with injective Frobenius map.

An ensemble Kalman filter for the time‐dependent analysis of the geomagnetic field

We present the application of the ensemble Kalman filter to a three‐dimensional, convection‐driven model of the geodynamo. Our implementation rests on a suitably modified version of the parallel data assimilation framework of Nerger and Hiller (2013). We resort to closed‐loop experiments for validation purposes, using a dynamo model of intermediate resolution. Observations for these experiments consist of spectral coefficients describing the surface poloidal magnetic field, with arbitrary truncation. Our synthetic tests demonstrate the efficacy and adaptivity of the method, provided the ensemble comprises members, in which case the typical spin‐up time we find for our system is . In case of a poor resolution of the observations, we find that the knowledge of the full covariance matrix describing the uncertainty affecting the spectral coefficients (as opposed to its sole diagonal) results in a much better estimate of the internal structure of the dynamo.

Comparison of Mixed-Effects Models for Skew-Normal Responses with an Application to AIDS Data: A Bayesian Approach

The potency of antiretroviral agents in AIDS clinical trials can be assessed on the basis of a viral response such as viral decay rate or change in viral load (number of HIV RNA copies in plasma). Linear, nonlinear, and nonparametric mixed-effects models have been proposed to estimate such parameters in viral dynamic models. However, there are two critical questions that stand out: whether these models achieve consistent estimates for viral decay rates, and which model is more appropriate for use in practice. Moreover, one often assumes that a model random error is normally distributed, but this assumption may be unrealistic, obscuring important features of within- and among-subject variations. In this article, we develop a skew-normal (SN) Bayesian linear mixed-effects (SN-BLME) model, an SN Bayesian nonlinear mixed-effects (SN-BNLME) model, and an SN Bayesian semiparametric nonlinear mixed-effects (SN-BSNLME) model that relax the normality assumption by considering model random error to have an SN distribution. We compare the performance of these SN models, and also compare their performance with the corresponding normal models. An AIDS dataset is used to test the proposed models and methods. It was found that there is a significant incongruity in the estimated viral decay rates. The results indicate that SN-BSNLME model is preferred to the other models, implying that an arbitrary data truncation is not necessary. The findings also suggest that it is important to assume a model with an SN distribution in order to achieve reasonable results when the data exhibit skewness.

Quantifying the hydraulic performance of treatment wetlands using reliability functions

Conventional water treatment is typically not practical for remediating non-point source water pollution and can be cost prohibitive even for point sources. Constructed wetlands are becoming an increasingly common best management practice for reducing pollutants. Time dependent treatment processes can be limited by hydraulic inefficiencies like short-circuiting in treatment wetlands. One reason the hydraulic effects on treatment are not well understood is that hydraulic inefficiencies are difficult to quantify. The aim of this work was to develop an objective measure of hydraulic performance in treatment wetlands. Such an index could be useful in determining the optimal wetland configuration to achieve the best level of treatment. The index would not only be useful in quantifying the effects of vegetation, bathymetry, and wetland shape on residence time; it could be used to provide the bounds for pollutant reduction. Hydraulic indices are typically derived from the residence time distribution. But most existing indices are unable to detect small variations or are not strongly related to treatment.Recognizing the close relationship between the residence time distribution and a probability density function, an approach rooted in failure analysis was used to provide a family of four unique functions derived from a single residence time distribution that can potentially provide new indices. Two hydraulic indices were derived with this approach. The new indices, the hazard index and temporal hazard index, were evaluated for their ability to detect variation and for their correlation to expected effluent pollutant fractions in order to assess their suitability as a predictor of treatment. The indices overcome several of the weaknesses inherent in other existing indices. Experimental constraints resulting in the arbitrary truncation of data have no impact on the proposed temporal hazard index. The hazard index and temporal hazard index could be useful for characterizing the effects on the flow regime from various wetland parameters like depth, bathymetry, and shape and also utilized as a predictor of effluent quality.

Design and Implementation of the Parameterized Multi-Standard High-Throughput Radix-4 Viterbi Decoder on FPGA

This paper presents a parameterized multi-standard adaptive radix-4 Viterbi decoder with high throughput and low complexity. The proposed Viterbi decoder supports constraint lengths ranging from 3-9, code rates in the range of 1/2-1/3, and arbitrary truncation lengths. We present a novel fabric of Add-Compare-Select Unit (ACSU) and methods of unsigned quantization and efficient normalization that shorten the critical path. The decoder achieves a low bit error ratio in multiple standards, such as GPRS, WiMax, LTE, CDMA, and 3G. The proposed decoder is implemented on Xilinx XC5VLX330 device and the frequency achieved is 181.7 MHz. The throughput of the proposed decoder can reach 363 Mbps, which is superior to the other current multi-standard Viterbi decoders or radix-4 Viterbi decoders on the FPGA platform. key words: multi-standard, radix-4, Viterbi decoder, FPGA