Scalar output

Analytical instrumentation in general can be defined by its output signal according to tensorial algebra. This algebraic approach characterizes different levels of data complexity and relates one level to another. A single output (scalar) is in the zero-order level. A vector output is in the first order and a matrix output is in the second order. Different mathematical advantages exist with each order... 

Each of the units has multiple inputs, which may be partly excitatory and partly inhibitory. The units usually obtain a weighted sum of all the inputs, which, as a single output, is passed down the axon analogue elements. The output scalar compares to the average spike rate of a neuron (Crick, 1989). 

In the LLM the (scalar) desired output value ( J w the actual (wrong) output value ... 

Under Marx s assumption, in Capital, volume 2, that prices and values are identical, and hence 1 of output is equal to an hour of labour time, this equation captures both an income and multiplier relationship. The equivalence between prices and values is embodied in the identity p = v such that the total employment of labour units (vQ) is equal to total money net income (pQ). Similarly, vF the total number of labour emits required to produce final demand, is equal to total money final demand (pF). Hence, the expression 1/1 — vh is an income/employment multiplier, in which the scalar vh represents the propensity to consume b, derived from the two-department schema.10 We shall refer to this as the Keyensian scalar multiplier, since although it is somewhat unusually defined according to worker consumption it retains the l/l h structure that is so common to economics textbooks. The simplicity of the Keynesian multiplier is retained in a two-department setting. 

It should be noted, however, that our application of the new interpretation does not imply that the traditional labour embodied definition of value should be completely abandoned. Foley (2000 30) is open to the possibility that there may be a role for both the new and traditional interpretations of the value of labour power. As Appendix 4 shows, the labour embodied definition of the value of labour power is nested in the input-output model of the circulation of money between departments of production, regardless of how prices are defined. The deviation of prices from values does not modify the constituent role of the labour embodied measure in the interindustry monetary circuit. It is only when a macroeconomic aggregation is developed under price-value deviations, and in the derivation of the scalar Keynesian multiplier, that a switch to the value-form definition is required. 

The result, obtained in Chapter 2, that Marx s category of surplus value can be identified as a constituent element of the Keynesian scalar multiplier, can also be derived for the Leontief matrix multiplier. Starting with the input-output identity... 

The relationship between final demand and gross output is specified according to the output matrix multiplier M = (I — A hi)-1. The structure of this output multiplier matrix can be examined by first considering the scalar employment multiplier. Since vQ = IX, the employment multiplier (2.23) can be written as... 

The Leontief output multiplier matrix M can be decomposed with the scalar e (the share of surplus value) as a constituent element. 

This type of scalar multiplier can also be derived from the two-sector Kaleckian schema, as shown by Nell (1988b 112), although this latter multiplier was not applied specifically to the circulation of money. A possible advantage of equation (4.23), since it is derived from an input-output model, is that it could be easily generalized to an n sector framework. 

A dipole and its scalar potential thus represent a true negative resistor system of the most fundamental kind. The dipole continually receives EM energy in unusable form (reactive power, which cannot perform real work), converts it to usable form (real power, which can perform real work), and outputs it as usable, real EM energy flow (real power) in 3-space. 

Starting at line 900 you find the user subroutine. In this routine the mole numbers occupy the array elements NW(1), NW(2),. .., NW(5) and the scalar variable NW stores the total mole number. At the current value X(l) and X(2) of the reaction extents we first calculate tine mole numbers. If any of them is negative or zero, the error flag ER is set to a nonzero value. If the mole numbers are feasible, the values computed according to (2.31) will occupy the array elements G(l) and G(2). The initial estimates are X(1) = 1 and X(2) = 0.1, the first corrections are D(l) = D(2) = 0.01. The following output shows some of the iterations. 

Our choice for the non-linear system approach to PARC is the ANN. The ANN is composed of many neurons configured in layers such that data pass from an input layer through any number of middle layers and finally exit the system through a final layer called the output layer. In Fig. 4 is shown a diagram of a simple three-layer ANN. The input layer is composed of numeric scalar data values, whereas the middle and output layers are composed of artificial neurons. These artificial neurons are essentially weighted transfer functions that convert their inputs into a single desired output. The individual layer components are referred to as nodes. Every input node is connected to every middle node, and every middle node is connected to every output node. 

Systems approach borrowed from the optimization and control communities can be used to achieve various other tasks of interest in multiscale simulation. For example, Hurst and Wen (2005) have recently considered shear viscosity as a scalar input/output map from shear stress to shear strain rate, and estimated the viscosity from the frequency response of the system by performing short, non-equilibrium MD. Multiscale model reduction, along with optimal control and design strategies, offers substantial promise for engineering systems. Intensive work on this topic is therefore expected in the near future. 

The "pipeline11 structure allows instructions to be processed concurrently in all levels of the pipe in both scalar and vector mode. The eight levels of the MBU-AU pair under optimum conditions can each produce an output every CPU clock cycle (80 nsec). Pipe levels unnecessary to a particular instruction are bypassed. Figure 1 also illustrates how different sections of the arithmetic pipeline are utilized for execution of a particular instruction, i.e., floating-point addition and fixed-point multiplication. 

The general formulation for a dynamic-programming problem, presented in a simplified form, is shown in Fig. 11-11. On the basis of the definitions of terms given in Fig. 11-lla, each of the variables, x1+1, xt, and dt, may be replaced by vectors because there may be several components or streams involved in the input and output, and several decision variables may be involved. The profit or return Pt is a scalar which gives a measure of contribution of stage i to the objective function. 

Define a family of -dimensional orthogonal parallelepipeds, P(a), self-similar among them, centered at the target value of the outputs (yo), where the scalar a affects each of their sizes by the following set of inequalities ... 

Large-eddy simulation output is a three-dimensional, time-dependent flow and scalar field. The results are unique in reproducing most aspects of the turbulent flow field and its interaction with a layer of vegetation. Due to the considerable demand on computational resources, it is not yet reasonable to utilize a grid network that can sufficiently resolve a vegetation canopy and, at the same time, extend both horizontally and vertically to simulate a full atmospheric boundary layer. Nevertheless, even simulations with quite limited vertical extent, as few as three canopy heights, have been successful in accurately reproducing the features described earlier. 

The specification of a simulation problem in CHEOPS is done by means of setup files in XML format which describe the structure of the flowsheet to be solved as well as variables of various types (scalars, vectors, time profiles, and distributions). The variables are classified into inputs, outputs, parameters, and states. Inputs and parameters should be specified by the user. The setup files define references to the models, their types and associated tools, and the type of simulation with a respective set of simulation options. 

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