Utility vector

Mathematical models require computation to secure concrete predictions. Successes in relatively simple cases spurs interest in more complex situations. Somewhat specialized computer hardware and software have emerged in response to these demands. Examples are the high-end processors with vector architecture, such as the Cray series, the CDC Cyber 205, and the recently announced IBM 3090 with vector attachment. When a computation can effectively utilize vector architecture, such machines will out-perform even the most powerful conventional scalar machine by a substantial margin. Such performance has given rise to the term supercomputer. ... 

Consumption vector. Consumption vector for species A. CA is the sum of the vectors for the rate of consumption of Resource 1 and Resource 2. The consumption vector determines the path of the concentrations of resources as it moves through the resource space. In the one-species case, the eventual equilibrium of resources occurs where the sum of the utilization vectors and the CA is zero. 

As host cells that have been successfully transformed proliferate, they rapidly amplify the recombinant DNA. For example, under favorable conditions of nutrient availability and temperature, a single recombinant plasmid introduced into an E. coli cell can be replicated a billion times in about 11 hours. However, transformed and untransformed cells usually have identical appearances. (See Figure 18C for an example of an exception to this mle.) Consequently, researchers often design cloning protocols utilizing vectors with selectable marker... 

Conservative assumptions Several conservative assumptions have been applied to the models previously described, as shown in the transition and cost matrices, and the utility vectors. These assumptions in effect set up the SBN with a definite handicap compared with the monolith spacecraft. Our purpose for doing so is to set up tough conditions under which SBN would compete against the monolith architecture, and should advantages result despite these conservative assumptions, the findings in favor of SBN would be more credible. In short, our conservative assumptions allow the assessment of the possible cost and utility benefits that are inherent to the fractionated nature of SBNs. The conservative assumptions are the following ... 

A utility vector is in the core if the total utility of every possible coalition is at least as large as the coalition s value, i.e., there does not exist a coalition of players that could make all of its members at least as well off and one member strictly better off. 

Linear combinations with more than two descriptors show an unsatisfactory-statistical behavior and a dramatically deteriorating utility vector. Thus, the modeling equation with two variables results in ... 

The Function unit Utility Vector(FUV) shows the number of necessary function units in each condition corresponding to CV components. The FUV is calculated for each FU (e.g. adder, ALU). FUV Sj is the sum of all actual CVs a for nodes which are allocated to a FU / in c-step k,... 

This control sequence synthesis technique has its roots in the global slicing technique in the Bridge system[17]. It is improved by using CVs. The sum of function unit utility vector for all nodes in step k (FUVALL 5, ) indicates the number of all kinds of operations to be executed in c-step k. Therefore, if some components of FUVALL are zero, no operation will be carried out in c-step k under the conditions corresponding to the 0 components of FUVs. Consequently, c-step k can be skipped under such conditions. 

The state number of the FMS for this control sequence is fewer than that synthesized by the conventional methods based on CFG transformation because the operations in different branches belong to the same states. The CV method is more effective for use of ALUs. For instance, in the case where FU utility vectors and are [1,1,3] and [2,1,0], three adders... 

The starting point for obtaining quantitative descriptions of flow phenomena is Newton s second law, which states that the vector sum of forces acting on a body equals the rate of change of momentum of the body. This force balance can be made in many different ways. It may be appHed over a body of finite size or over each infinitesimal portion of the body. It may be utilized in a coordinate system moving with the body (the so-called Lagrangian viewpoint) or in a fixed coordinate system (the Eulerian viewpoint). Described herein is derivation of the equations of motion from the Eulerian viewpoint using the Cartesian coordinate system. The equations in other coordinate systems are described in standard references (1,2). 

Plasmid Vectors for Facile Introduction of Passenger DNA and Selection of Recombinants. The map of a commonly used plasmid vector, pUC19 (7), is shown in Figure 2. Three parts of the vector are key to its utility. The origin sequence, oh, allows the repHcation of plasmid DNA in high copy number relative to the chromosome. A gene, amp, encoding the enzyme beta-lactamase, which hydrolyzes penicillin compounds, allows... 

Loops that could not be vectorized on conventional vector computers often performed very well under the Multiflow architecture and, unlike vector machines, for which a person could spend a great deal of time optimizing programs, substantially less could be done on the Multiflow, as most of the work fell to the compiler anyway. All the usual optimizations for memory utilization and cache usage also appHed to the Microflow. There were, of course, programs for which the compiler could not make good use of the multiple functional units, and the computer would mn at the speed of just one or two iadividually quite slow functional units. 

Certainly the most prominent feature of the breakdown process is its dependence on the polarity of the electric field relative to the shock-velocity vector. This effect is manifest in current pulse anomalies from minus-x orientation samples or positively oriented samples subjected to short-pulse loading (see Fig. 4.8). The individual effects of stress and electric field may be delineated with short-pulse loadings in which fields can be varied by utilizing stress pulses of various durations [72G03]. 

The classical scheme for dichroism measurements implies measuring absorbances (optical densities) for light electric vector parallel and perpendicular to the orientation of director of a planarly oriented nematic or smectic sample. This approach requires high quality polarizers and planarly oriented samples. The alternative technique [50, 53] utilizes a comparison of the absorbance in the isotropic phase (Dj) with that of a homeotropically oriented smectic phase (Dh). In this case, the apparent order parameter for each vibrational oscillator of interest S (related to a certain molecular fragment) may be calculated as S = l-(Dh/Di) (l/f), where / is the thermal correction factor. The angles of orientation of vibrational oscillators (0) with respect to the normal to the smectic layers may be determined according to the equation... 

HPLC has also been utilized in more complex food chain transfers. It has been known for some time that the toxins can be responsible for fish kills in the Bay of Fundy 18). The vectors for these fish kills are zooplankton that feed on toxic dinoflagellates. In two related studies (79 Sullivan, unpublished), HPLC was utilized to investigate the transport of toxins from dinoflagellates to zooplankton and then to fish. The HPLC method is ideally suited for this since only very small sample sizes (ca. 100,000 dinoflagellate cells) are required. 

For example, the ZN theory, which overcomes all the defects of the Landau-Zener-Stueckelberg theory, can be incorporated into various simulation methods in order to clarify the mechanisms of dynamics in realistic molecular systems. Since the nonadiabatic coupling is a vector and thus we can always determine the relevant one-dimensional (ID) direction of the transition in multidimensional space, the 1D ZN theory can be usefully utilized. Furthermore, the comprehension of reaction mechanisms can be deepened, since the formulas are given in simple analytical expressions. Since it is not feasible to treat realistic large systems fully quantum mechanically, it would be appropriate to incorporate the ZN theory into some kind of semiclassical methods. The promising semiclassical methods are (1) the initial value... 

Returning to the unit-ceU, we can also utilize the vector method to derive the origin of the Miller Indices. The general equation for a plane in the lattice is ... 

The covariance criterion as such suggests a symmetrical situation, X and Y playing equivalent roles. In fact, up to here, there is little difference with Procrustes analysis which also utilizes the singular vectors of the covariance matrix (Section 35.2). The difference is that in PLS the first X-factor, say tj, is now used as a regressor to fit both the X-block and the T-block ... 

In a completed map, every unit should have a similar probability of being the winning emit for a sample picked at random from the dataset. However, as the map evolves and the weights vectors adjust, the utility of an individual unit may change. Because the signal counter or the local errors are reduced every epoch by a small fraction, the value of this measure for units that are very rarely selected as BMUs will diminish to a value close to zero, indicating that these units contribute little to the network and, therefore, can be pruned out. 

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