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Glycoproteins present in the soluble and organelle fractions of developing bean (Phaseolus vulgaris) cotyledons were analyzed by sodium dodecyl sulfate-polyacrylamide gel electrophoresis, affinoblotting, fractionation on immobilized concanavalin A (ConA), and digestion of the oligosaccharide side chains with specific glycosidases before and after protein denaturation. These studies led to the following observations. (a) Bean cotyledons contain a large variety of glycoproteins that bind to ConA. Binding to ConA can be eliminated by prior digestion of denatured proteins with alpha-mannosidase or endoglycosidase H, indicating that binding to ConA is mediated by high-mannose oligosaccharide side chains. (b) Bean cotyledons contain a large variety of fucosylated glycoproteins which bind to ConA. Because fucose-containing oligosaccharide side chains do not bind to ConA, such proteins must have both high-mannose and modified oligosaccharides. (c) For all the glycoproteins examined except one, the high-mannose oligosaccharides on the undenatured proteins are accessible to ConA and partially accessible to jack bean alpha-mannosidase. (d) Treatment of the native proteins with alpha-mannosidase removes only 1 or 2 mannose residues from the high-mannose oligosaccharides. Similar treatments of sodium dodecyl sulfate-denatured or pronase-digested glycoproteins removes all alpha-mannose residues. The results support the following conclusions: certain side chains remain unmodified as high-mannose oligosaccharides even though the proteins to which they are attached pass through the Golgi apparatus, where other oligosaccharide chains are modified. The chains remain unmodified because they are not accessible to processing enzymes such as the Golgilocalized alpha-mannosidase.

HiGHS is high performance serial and parallel software for solving large-scale sparse linear programming (LP), mixed-integer programming(MIP) and quadratic programming (QP) models, developed in C++11, withinterfaces to C, C#, FORTRAN, Julia and Python.

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HiGHS is based on the high performance dual revised simpleximplementation (HSOL) and its parallel variant (PAMI) developed by QiHuangfu. Features such as presolve, crash and advanced basis starthave been added by Julian Hall and Ivet Galabova. The QP solver andoriginal language interfaces were written by Michael Feldmeier. LeonaGottwald wrote the MIP solver. The software engineering of HiGHS wasdeveloped by Ivet Galabova.

No matter which tremolo pattern you use, one of the basic requirements to produce an effortless and accurate tremolo is to make small finger movements. The range of motion must be short. If your fingers make large follow through motions or begin their stokes far from the string or high above the string, you are asking for trouble. Obviously, the further the finger is from the string the greater the chance of missing the string entirely or not hitting the sweet spot of flesh/nail contact. The greater the distance each finger has to travel, the more difficult it will be to play fast. The same holds true for the thumb. Although speed is not an issue for the thumb in the tremolo, accuracy and tone quality certainly are.

Although a few exceptions can be found, in most tremolo passages in the repertoire, the fingers carry the melody and the thumb plays the accompaniment. Therefore, when practicing any of the tremolo exercises in this article, it is important to train the thumb to play quietly. As the speed of an exercise is increased, the thumb naturally will tend to play louder. It becomes more difficult to curb this tendency at fast speeds. For this reason, when practicing these exercises at the recommended slow starting speeds, the thumb should play pianissimo or pianississimo. Then, as you reach tremolo speeds of MM=144+ the balance between thumb and fingers will be correct. Proper balance of volume between the thumb and fingers is an essential element of a good tremolo.

Meet or surpass your top speed every day. Keep track of your speeds. Write them down. This is precision work. Remember, never begin at too fast a starting speed that could produce tension in the hand or fingers.

Two main factors motivated the work in this paper to develop a parallelisation of the dual revised simplex method for standard desktop architectures. Firstly, although dual simplex implementations are now generally preferred, almost all the work by others on parallel simplex has been restricted to the primal algorithm, the only published work on dual simplex parallelisation known to the authors being due to Bixby and Martin [1]. Although it appeared in the early 2000s, their implementation included neither the BFRT nor hyper-sparse linear system solution techniques so there is immediate scope to extend their work. Secondly, in the past, parallel implementations generally used dedicated high performance computers to achieve the best performance. Now, when every desktop computer is a multi-core machine, any speedup is desirable in terms of solution time reduction for daily use. Thus we have used a relatively standard architecture to perform computational experiments.

A worthwhile simplex parallelisation should be based on a good sequential simplex solver. Although there are many public domain simplex implementations, they are either too complicated to be used as a foundation for a parallel solver or too inefficient for any parallelisation to be worthwhile. Thus the authors have implemented a sequential dual simplex solver (hsol) from scratch. It incorporates sparse LU factorization, hyper-sparse linear system solution techniques, efficient approaches to updating LU factors and sophisticated dual revised simplex pivoting rules. Based on components of this sequential solver, two dual simplex parallel solvers (pami and sip) have been designed and developed.

Section 2 introduces the necessary background, Sects. 3 and 4 detail the design of pami and sip respectively and Sect. 5 presents numerical results and performance analysis. Conclusions are given in Sect. 6.

This section introduces all the necessary background knowledge for developing the parallel dual simplex solvers. Section 2.1 introduces the computational form of LP problems and the concept of primal and dual feasibility. Section 2.2 describes the regular dual simplex method algorithm and then details its key enhancements and major computational components. Section 2.3 introduces suboptimization, a relatively unknown dual simplex variant which is the starting point for the pami parallelisation in Sect. 3. Section 2.4 briefly reviews several existing simplex update approaches which are key to the efficiency of the parallel schemes.

For the purpose of this report, advanced chuzc can be viewed as having two stages, an initial stage chuzc1 which simply accumulates all candidate nonbasic variables and then a recursive selection stage chuzc2 to choose the entering variable q from within this set of candidates using BFRT and the Harris two-pass ratio test. chuzc also determines the primal step \(\theta _p\) and dual step \(\theta _q\), being the changes to the primal basic variable p and dual variable q respectively. Following a successful BFRT, chuzc also yields an index set \({\mathcal {F}}\) of any primal variables which have flipped from one bound to the other.

Although the direct update of the basis inverse from \(B_k^{-1}\) to \(B_{k+t}^{-1}\) can be achieved easily via the PF or APF update, in terms of efficiency for future simplex iterations, the collective FT update is preferred to the PF and APF updates. The value of the APF update within pami is indicated in Sect. 3.

This section introduces the design and implementation of the parallel dual simplex scheme, pami. It extends the suboptimization scheme of Rosander [21], incorporating (serial) algorithmic techniques and exploiting parallelism across multiple iterations.

The concept of pami was introduced by Hall and Huangfu [9], where it was referred to as ParISS. This prototype implementation was based on the PF update and was relatively unsophisticated, both algorithmically and computationally. Subsequent revisions and refinements, incorporating the advanced algorithmic techniques outlined in Sect. 2 as well as FT updates and some novel features introduced in this section, have yielded a very much more sophisticated and efficient implementation. Specifically, our implementation of pami out-performs ParISS by almost an order of magnitude in serial and to achieve the speed-up demonstrated in Sect. 5 has required new levels of task parallelism and parallel algorithmic control techniques described in Sects. 3.2 and 3.3, in addition to the linear algebra techniques introduced by Huangfu and Hall in [16].

Section 3.1 provides an overview of the parallelisation scheme of pami and Sect. 3.2 details the task parallel ftran operations in the major update stage and how to simplify it. A novel candidate quality control scheme for the minor optimality test is discussed in Sect. 3.3.

The major optimality test involves only major chuzr operations in which s candidates are chosen (if possible) using the DSE framework. In pami the value of s is the number of processors being used. It is a vector-based operation which can be easily parallelised, although its overall computational cost is not significant since it is only performed once per major operation. However, the algorithmic design of chuzr is important and Sect. 3.3 discusses it in detail.

The minor ratio test is a major source of parallelisation and performance improvement. Since the btran result is known (see below), the minor ratio test consists of spmv, chuzc1 and chuzc2. The spmv operation is a sparse matrix-vector product and chuzc1 is a one-pass selection based on the result of spmv. In the actual implementation, they can share one parallel initialisation. On the other hand, chuzc2 often involves multiple iterations of recursive selection which, if exploiting parallelism, requires many synchronisation operations. According to the component profiling in Table 1, chuzc2 is a relative cheap operation thus, in pami, it is not parallelised. Data parallelism is exploited in spmv and chuzc1 by partitioning the variables across the processors before any simplex iterations are performed. This is done randomly with the aim of achieving load balance in spmv. e24fc04721