Forward Substitution Research Articles

In search of a substitution model for coca in Colombia: Buffalo, cocoa, and coffee in Peasant Reserve Zones

AbstractFor years Colombia has been the world's largest coca producer. Its public management of crops for illicit use has swung between eradication, substitution, and, recently legalization. Forced eradication has been shown to be ineffective, and legalization is an incipient option, so the Peace Agreement puts forward substitution as the path to follow. Yet, what kind of substitution does it suggest? This article analyzes voluntary substitution projects in Peasant Reserve Zones. While some projects have evolved locally due in part to strong peasant associations, they have not gained traction nationally. In general, the difficulties inherent in any business play a role, but there are also structural limitations such as continued fumigations, obligations of prior eradication, the costs of production and transportation due to the lack of infrastructure and public services, and the issue of land rights, which limits peasants' access to the formal funding established by the Peace Agreement.

PaScaL_TDMA 2.0: A multi-GPU-based library for solving massive tridiagonal systems

PaScaL_TDMA 2.0: A multi-GPU-based library for solving massive tridiagonal systems

Iterative Method of Thomas Algorithm on The Case Study of Energy Equation

Implicit method is one of the finite difference method and is widely used for discretization some of ordinary or partial differential equations, such like: advection equation, heat transfer equation, burger equation, and many others. Implicit method is unconditionally stable and has been proved with the approximation of Von-Neumann stability criterion. Actually, implicit method is always identical to block matrices (tri-diagonal matrices or penta-diagonal matrices). These matrices can be solved numerically by Thomas algorithm including Gauss elimination using pivot or not, backward or forward substitution. Furthermore, it can be also solved using LU decomposition method with the elimination of lower triangle matrices first and then the elimination of upper triangle matrices. In this research, Thomas algorithm is used to solve numerically for the problem of convective flow on boundary layer, especially for energy equation with the variation of Prandtl number ( ).

Derivatization and biological activity studies of 3-chloro-3-chlorosulfenyl spiro tetrahydropyran/tetrahydrothiopyran-4,2'-chroman-4'-one

The adducts 4a,b-7a , b have been obtained either by reducing α-chloro-β-oxosulfenyl chlorides 2a,b with iodide ion in the presence of dienes namely, 2-methyl-1,3-butadiene (isoperene), 2,3-dimethyl-1,3-butadiene, 1,2,3,4-tetrachlorocyclopentadiene, or 1,3-cyclohexadiene, respectively; or by thermolysis of oxadithiin derivatives 3a,b in the presence of the same aforementioned dienes presumably via the formation of the same intermediate A in both cases of compounds 2a,b and 3a,b . It is observed that α-chloro-β-oxosulfenyl chlorides 2a,b undergo straight forward substitution with potassium cyanide to give 8a,b . Direct oxidation of 2a,b with H 2 O 2 /AcOH affords 3,3-dichloropyran-4-ones 9a,b , while conversion of 2a,b to the sulfonamides 10a,b followed by oxidation provides 3-chloropyranones 11a,b . Antioxidant and antimicrobial evaluation of compounds 4a,b-6a,b shows moderate activiy. MIC of the derivative 6b reveals a remarkable inhibition of the pathogenic gram positive bacteria ( Staphylococcus aureus ) as well as gram negative E coli .

A block forward substitution method for solving the hypercomplex finite element system of equations

The hypercomplex finite element method, ZFEM, allows the analyst to compute highly-accurate arbitrary-order shape, material property, and loading derivatives by augmenting the traditional finite element method with multiple imaginary degrees of freedom. In ZFEM, the real variables are converted to hypercomplex variables such as multicomplex, multidual, or quaternions. By uplifting the real variables to hypercomplex, derivatives are computed in an automated fashion using a standard finite element formulation. The use of multicomplex or multidual numbers provides higher-order derivatives. The drawback of ZFEM is that it increases the number of degrees of freedom of the real variable system by a factor 2n, where n is the order of the required derivative. In consequence, ZFEM increases the memory consumption and the solution time of the system of equations compared to the real variable system. The block forward substitution method (BFS), proposed in this work, addresses the memory and runtime issues. This new method solves the original real-valued FEM system once. Then, the derivatives are computed using pseudo-loads with the original system of equations. In contrast with the conventional solution method of ZFEM, BFS computes the hypercomplex contributions to the stiffness matrix element-wise, and it never assembles nor solves the full hypercomplex system of equations. In effect, the BFS method generalizes the first-order semi-analytical complex variable method to any order derivative. The BFS method provides the capability to allow a combination of real-variable and hypercomplex-variable elements within the same model. The numerical results indicate that a first-order derivative can be obtained with 1% to 8% additional computational time of the real-variable analysis. This allows the computation of multiple first-order derivatives by post-processing of a single FEM analysis. Additionally, it was shown that fourth-order shape sensitivities can be computed in less than 5% additional runtime of the real-variable FEM analysis.

Algebraic Solution of Tropical Polynomial Optimization Problems

We consider constrained optimization problems defined in the tropical algebra setting on a linearly ordered, algebraically complete (radicable) idempotent semifield (a semiring with idempotent addition and invertible multiplication). The problems are to minimize the objective functions given by tropical analogues of multivariate Puiseux polynomials, subject to box constraints on the variables. A technique for variable elimination is presented that converts the original optimization problem to a new one in which one variable is removed and the box constraint for this variable is modified. The novel approach may be thought of as an extension of the Fourier–Motzkin elimination method for systems of linear inequalities in ordered fields to the issue of polynomial optimization in ordered tropical semifields. We use this technique to develop a procedure to solve the problem in a finite number of iterations. The procedure includes two phases: backward elimination and forward substitution of variables. We describe the main steps of the procedure, discuss its computational complexity and present numerical examples.

A Hamiltonian decomposition for fast interior-point solvers in model predictive control

Optimal decision-making tools are essential in industry to achieve high performance. One of these tools is model predictive control (MPC), which is an advanced control technique that generates an action that affects the controlled variables, while satisfying the process’ operational constraints. At the core of the MPC algorithm lies an optimization problem that is solved by a numerical method at every sample time. New demand for more self-contained modular processes has seen MPC embedded in small-scale platforms. This has prompted a need for custom-made numerical methods that help to run the computationally demanding optimization algorithms efficiently. In this paper, we propose two approaches that factorize the Newton system of the interior-point method based on the two-point boundary-value problem structure, rarely explored in MPC. By exploiting the Hamiltonian form of the augmented system, we derive an incomplete LU factorization. A direct method is available to compute the solution of the system using a forward substitution of a series of matrices. We also propose a preconditioned Krylov method that converges within a small number of iterations only depending on the number of states.

Tree/link method for transfer function and stability analysis of switched‐capacitor circuits

SummaryThe wide spread application of switched‐capacitor circuits has resulted in complex structures wherein the derivation of transfer function in discrete form is not quite straight forward. A computer‐aided tool for direct transfer function analysis of switched‐capacitor circuits using state formulation method is proposed in this paper. The state equation matrices are directly constructed from the circuit topology using tree/link analysis. The entire topology is formulated only using cutset equations to obtain the state matrices without any modifications. The discretized topological state matrices are used to generate the transfer function in z form by forward substitution of state equation in successive clock phase. Lyapunov criteria‐based matrix equation constructed using the same state matrix is used to investigate the circuit stability. The formulation is also suitable in addressing the effect of non‐idealities like switch resistance and finite gain of operational amplifiers, on the location of poles and zeros. Various numerical examples have been presented to demonstrate the performance of the simulator.

Flexible 5G New Radio LDPC Encoder Optimized for High Hardware Usage Efficiency

Quasi-cyclic low-density parity-check (QC–LDPC) codes are introduced as a physical channel coding solution for data channels in 5G new radio (5G NR). Depending on the use case scenario, this standard proposes the usage of a wide variety of codes, which imposes the need for high encoder flexibility. LDPC codes from 5G NR have a convenient structure and can be efficiently encoded using forward substitution and without computationally intensive multiplications with dense matrices. However, the state-of-the-art solutions for encoder hardware implementation can be inefficient since many hardware processing units stay idle during the encoding process. This paper proposes a novel partially parallel architecture that can provide high hardware usage efficiency (HUE) while achieving encoder flexibility and support for all 5G NR codes. The proposed architecture includes a flexible circular shifting network, which is capable of shifting a single large bit vector or multiple smaller bit vectors depending on the code. The encoder architecture was built around the shifter in a way that multiple parity check matrix elements can be processed in parallel for short codes, thus providing almost the same level of parallelism as for long codes. The processing schedule was optimized for minimal encoding time using the genetic algorithm. The optimized encoder provided high throughputs, low latency, and up-to-date the best HUE.

Summary of Research on Power Flow Optimization Algorithms for Microgrid

With the development of microgrid, more and more scholars have participated in the optimization research of microgrid power flow. This article mainly summarizes the algorithms for power flow optimization of microgrid, including the Newton-Raphson method, PQ decomposition method, nonlinear programming power flow algorithm, interior point method, forward and backward substitution method, and artificial intelligence algorithms such as particle swarm algorithm, genetic algorithm, simulated annealing and various hybrid algorithms.

Using Parameter Elimination to Solve Discrete Linear Chebyshev Approximation Problems

We consider discrete linear Chebyshev approximation problems in which the unknown parameters of linear function are fitted by minimizing the least maximum absolute deviation of errors. Such problems find application in the solution of overdetermined systems of linear equations that appear in many practical contexts. The least maximum absolute deviation estimator is used in regression analysis in statistics when the distribution of errors has bounded support. To derive a direct solution of the problem, we propose an algebraic approach based on a parameter elimination technique. As a key component of the approach, an elimination lemma is proved to handle the problem by reducing it to a problem with one parameter eliminated, together with a box constraint imposed on this parameter. We demonstrate the application of the lemma to the direct solution of linear regression problems with one and two parameters. We develop a procedure to solve multidimensional approximation (multiple linear regression) problems in a finite number of steps. The procedure follows a method that comprises two phases: backward elimination and forward substitution of parameters. We describe the main components of the procedure and estimate its computational complexity. We implement symbolic computations in MATLAB to obtain exact solutions for two numerical examples.

Developing benign syntheses using ion pairs via solvent-free mechanochemistry

Solvent-free mechanochemical conditions have been developed to investigate the significance of ion pairing and the use of weak bases for driving forward nucleophilic substitution reactions.

BAX: A Bundle Adjustment Accelerator With Decoupled Access/Execute Architecture for Visual Odometry

As the demand for embedded-vision grows, solving large optimization problems in real-time with energy and cost budget is a challenge. We present BAX, a hardware accelerator of bundle adjustment (BA), which solves the least-squares problem of state estimation in visual odometry (VO). BAX consists of a frontend and a backend for control and computation, respectively. The frontend generates instructions on-the-fly executed at the backend to perform the BA algorithm. The backend adopts decoupled access/execute (DAE) architecture, which separates the memory access unit (MAU) from the pipeline. The MAU can prefetch vectors and matrices ahead of computations. To further reduce the latency of data reorganization, three transpose-free dataflows are proposed for matrix multiplication operations on the vector processing unit (VPU). Besides, a unified architecture for both forward and backward substitution is designed for matrix decomposition in the linear solver. All the data are stored in 442kB on-chip memory, and the local map is maintained efficiently by the hierarchical graph memory. Compared with the baseline architecture, the processing time is reduced by 53.9% through the above techniques. BAX is implemented in 32-bit floating-point precision with data normalization on FPGA. It completes a full BA in about 63.44ms at 200MHz, consuming 1.12W power. BAX is $1.73\times $ and $22.38\times $ faster than the desktop and embedded CPUs, respectively, and achieves 90% performance of the GPU at much less power consumption.

Parallel Algorithms for Forward and Back Substitution in Linear Algebraic Equations of Finite Element Method

Parallel Algorithms for Forward and Back Substitution in Linear Algebraic Equations of Finite Element Method

Algorithms and algebraic solutions of decay chain differential equations for stable and unstable nuclide fractionation

Radioactive decay processes, such as alpha decay, produce decay chains where the mass numbers of nuclides decrease as larger nuclides expel energetic particles to form smaller nuclides. Under these conditions, the coefficient matrix that describes the differential rate expressions for radioactive decay can be made lower triangular. With this special structure, formulating an algebraic solution to the decay chains can be done by first formulating the eigenvectors that make up the coefficient matrix, which can then be solved using forward substitution for a lower triangular matrix. This work details the derivation of algebraic solutions for decay chains of any number of stable and unstable nuclides with any number of branching based on this eigenvector analysis. A prototype computational code was developed to validate and compare this methodology against a number of other methods for solving similar systems. A two-phase sorting algorithm yielding the lower triangular matrix structure was established to apply the developed algebraic solutions for decay chains involving beta-emitting radionuclides transformed into daughter nuclides without change in their mass number. The methodologies produced in this work provide an efficient way to estimate nuclide fractions from natural decay processes.

Efficient use of sparsity by direct solvers applied to 3D controlled-source EM problems

Controlled-source electromagnetic (CSEM) surveying becomes a widespread method for oil and gas exploration, which requires fast and efficient software for inverting large-scale EM datasets. In this context, one often needs to solve sparse systems of linear equations with a large number of sparse right-hand sides, each corresponding to a given transmitter position. Sparse direct solvers are very attractive for these problems, especially when combined with low-rank approximations which significantly reduce the complexity and the cost of the factorization. In the case of thousands of right-hand sides, the time spent in the sparse triangular solve tends to dominate the total simulation time, and here we propose several approaches to reduce it. A significant reduction is demonstrated for marine CSEM application by utilizing the sparsity of the right-hand sides (RHS) and of the solutions that results from the geometry of the problem. Large gains are achieved by restricting computations at the forward substitution stage to exploit the fact that the RHS matrix might have empty rows (vertical sparsity) and/or empty blocks of columns within a non-empty row (horizontal sparsity). We also adapt the parallel algorithms that were designed for the factorization to solve-oriented algorithms and describe performance optimizations particularly relevant for the very large numbers of right-hand sides of the CSEM application. We show that both the operation count and the elapsed time for the solution phase can be significantly reduced. The total time of CSEM simulation can be divided by approximately a factor of 3 on all the matrices from our set (from 3 to 30 million unknowns, and from 4 to 12 thousands RHSs).

GPU-accelerated sparse matrices parallel inversion algorithm for large-scale power systems

State-of-the-art Graphics Processing Unit (GPU) has superior performances on float-pointing calculation and memory bandwidth, and therefore has great potential in many computationally intensive power system applications, one of which is the inversion of large-scale sparse matrix. It is a fundamental component for many power system analyses which requires to solve massive number of forward and backward substitution (F&B) subtasks and seems to be a good GPU-accelerated candidate application. By means of solving multiple F&B subtasks concurrently and a serial of performance tunings in compliance with GPU’s architectures, we successfully develop a batch F&B algorithm on GPUs, which not only extracts the intra-level and intra-level parallelisms inside single F&B subtask but also explores a more regular parallelism among massive F&B subtasks, called inter-task parallelism. Case study on a 9241-dimension case shows that the proposed batch F&B solver consumes 2.92 μs per forward substitution (FS) subtask when the batch size is equal to 3072, achieving 65 times speedup relative to KLU library. And on the basis the complete design process of GPU-based inversion algorithm is proposed. By offloading the tremendous computational burden to GPU, the inversion of 9241-dimension case consumes only 97 ms, which can achieve 8.1 times speedup relative to the 12-core CPU inversion solver based on KLU library. The proposed batch F&B solver is practically very promising in many other power system applications requiring solving massive F&B subtasks, such as probabilistic power flow analysis.

New bio-based copolyesters derived from 1,4-butanediol, terephthalic acid and 2,5-thiophenedicarboxylic acid: Synthesis, crystallization behavior, thermal and mechanical properties

A series of 2,5-thiophenedicarboxylic acid-based copolyesters (PBTTFs) were synthesized from 2,5-thiophenedicarboxylic acid (TFDCA), terephthalic acid (TA) and 1,4-butanediol (BDO). A straight forward partial substitution of non-renewable TA by renewable TFDCA was successfully done. The effects of composition on microstructure, crystallization behavior, thermal properties, and mechanical properties were investigated. When the content of TFDCA varied from 0 to 25%, the elongation at break varied from 9.1% to 348%. When the content of TFDCA was 75%, the tensile strength was 39.3 MPa and the elongation at break was 1223%. In summary, TFDCA can toughen poly(butylene terephthalate) (PBT) to the extent. For PBTTF25, PBTTF50, PBTTF75 and PBTTF87.5, the isodimorphic cocrystallization was observed. Additionally, DSC and WAXD results suggested the butylene terephthalate (BT) unit had the stronger crystallization ability compared to the butylene 2,5-thiophenedicarboxylate (BTF) unit.

Survey and Review

The Survey and Review article in this issue is “A Class of Iterative Solvers for the Helmholtz Equation: Factorizations, Sweeping Preconditioners, Source Transfer, Single Layer Potentials, Polarized Traces, and Optimized Schwarz Methods,” by Martin J. Gander and Hui Zhang. The Helmholtz equation appears in the study of time-harmonic waves \(u(x) \exp(-iømega t)\) arising in acoustics, electromagnetism, and other fields. In its simplest form the equation reads \((\Delta+k^2) u = f\), where (\Delta\) denotes the Laplacian operator and the constant \(k\) is the wavenumber, and therefore is reminiscent of the Poisson equation (\Delta u =f\). However, this similarity is only superficial, and the numerical solution of boundary value problems, often posed in unbounded domains, involving the Helmholtz equation is challenging. Classical iterative solvers are not suitable, and the recent literature has devoted much effort to the development of novel solvers. New iterative methods have been suggested by authors with a wide range of backgrounds and motivations and invoke different discretization strategies; some of them have been formulated at the linear algebra level and others at the level of the differential equation. Gander and Zhang survey the new developments using a unifying point of view. The main insight is given in section 2: the forward and backward substitution sweeps of the block LU factorization of the discrete system correspond at the continuous level to sweeps from left to right and right to left of an optimal Schwarz domain decomposition method. The article will be useful not only to those working directly with the Helmholtz and related partial differential equations, but also to anybody interested in iterative solvers for large linear systems.

Exact Solution of Sparse Linear Systems via Left-Looking Roundoff-Error-Free LU Factorization in Time Proportional to Arithmetic Work

The roundoff-error-free (REF) LU factorization, along with the REF forward and backward substitution algorithms, allows a rational system of linear equations to be solved exactly and efficiently. T...