Benchmarking model

Among them, Li-i-HP can be considered a benchmark model system [29, 30] because its low number of electrons makes possible to calculate accurate PES s. Its electronic spectrum has been meassured by Polanyi and coworkers [22], and has been recently very nicely reproduced using purely adiabatic PES s [31]. In the simulation of the spectrum[31], the transition lines were artificially dressed by lorentzians which widths were fitted to better reproduce the experimental envelop. The physical origin of such widths is the decay of the quasibound states of the excited electronic states through electronic predissociation (EP) towards the ground electronic state. This EP process is the result of the non-adiabatic cou-... 

Even CCSDT is not capable of adequately describing certain doubly excited states, and several extensions that incorporate connected quadruple excitations (i.e. methods that include T4 in the ground state) have been implemented. Unless some restrictions are placed on the subspaces for which quadruple excitations are possible, methods such as EOM-CCSDTQ will not be practical in other than benchmark model calculations. Such calculations are, of course, of some importance since one can calibrate approximate treatments of quadruple excitations by comparisons with the full EOM-CCSDTQ method, for example. Even higher excitation levels have been implemented and compared with FCI results [48-51], Again, these methods are not expected to be generally applicable to anything other than a model system, but they are of great value as benchmarks. 

Morse clusters are a potentially more interesting benchmark model system, offering an additional parameter to tune the interaction distance. They were used by Roberts et al. [64] to verify the correct functioning of their EA implementation, up to =50 better performance than by a random search was also demonstrated. 

Budtz-Jorgensen, E., N. Keiding, and P. Grandjean. 1999. Benchmark Modeling of the Faroese Methylmercury Data. Research Report 99/5. Prepared at the University of Copenhagen, Denmark for the U.S. Environmental Protection Agency. 

Kirtman et al.248 use ab initio methods to benchmark model calculations in which a bundle of hexatriene molecules is intended to simulate polyacetylene. They find that the effect of the medium can be accurately reproduced by... 

This often used benchmark model is represented by the symmetrically stretched H2O molecule at the DZ level, for which the exact FCI results are available (35). In addition to the standard L-CCSD and CCSD correlation energies, we present the results obtained with RMR CCSD and four of its AL versions (Table 5). Similarly as for the S4 model, we employ two different reference spaces the minimal (2,2) space, involving HOMO and LUMO, and the (4,4) space involving four electrons in four orbitals (2 occupied and 2 virtual ones). For an easier comparison, we also present the corresponding differences from the FCI result in parentheses. 

Reengineering tools include benchmarking, modeling and analysis tools, simulation, and activity-based costing. 

There is still a consistency problem if we want to price interest rate derivatives on zero bonds, like caplets or floorlets, and on swaps, like swaptions, at the same time within one model. The popular market models concentrate either on the valuation of caps and floors or on swaptions, respectively. Musiela and Rutkowski (2005) put it this way We conclude that lognormal market models of forward LIBORs and forward swap rates are inherently inconsistent with each other. A challenging practical question of the choice of a benchmark model for simultaneous pricing and hedging of LIBOR and swap derivatives thus arises. ... 

For example, the benchmark models were generated by the authors specifically to permit the use of homogeneous computations. The critical size was adjusted to allow for the reactivity-advantage from heterogeneity, and thus the calculated k should be unity if the multigroup cross sections used are correct. However, this is the only parameter where the correlation of calculation against experiment is certain even under these ideal... 

In this chapter, the performanees of four controllers (i.e., passive, PID, LQG, and neuromorphic controls) are compared to demonstrate the effectiveness of the proposed hybrid neuromorphic controller for hazard mitigation of civil structures while the uncontrolled structure is used as a baseline. Properties ofthethree-story building employing an MR damper are adopted from a benchmark model (Dyke et al. 1996). The mass of each floor = ni = =98.3 kg, the stiffness of each... 

To demonstrate the accuracy of eqn (12.26) together with eqn (12.30) and its boundary condition eqn (12.31), called the quantum Kramers-like theory, we use a symmetric spin-boson model as a concrete system. In this benchmark model, the nuclear vibrational motions are characterized by the Ohmic spectral density ... 

The final party affected by operational accidents is bystanders who live or work next to railroad lines. These people are strangers to the railroad in that they do not have any contractual arrangements with the railroad and cannot directly influence the probability of an accident. Yet they can suffer externalities as a result of operational accidents. Typically one bystander is killed each year, and about 9,000 people a year have to be evacuated from areas surrounding accidents involving cars carrying hazardous materials. The costs to bystanders will be denoted by e(x) per unit of transportation. These costs will be a decreasing function of the level of preventive effort undertaken by the railroad. The benchmark model will assume... 

In the normal good case where there is declining marginal valuation of safety as output expands, it is clear that profit maximization will lead to a lower level of safety than in the benchmark model. This is because the valuation given to a change in safety by the marginal customer will always be less than the average valuation by all of the customers. 

It should be remembered that profit maximization unequivocally results in a lower level of output than the benchmark model. Market power leads to some customers being priced out of the market. Even those customers who do remain in the market will suffer reduced consumer surplus as the monopolist extracts this surplus in profit. Therefore the biggest outcry by customers will not be on the basis that safety has been affected, but rather because prices have risen and some of them have been priced out of the market. 

The benchmark model will be modified by introducing a parameter a on the x variable in the customers utility function. This parameter represents customers perceptions of the preventive efforts undertaken by the railroad. If customers are perfectly informed, as in the benchmark model, the parameter will take the value of one. A value of a of greater than one indicates that customers perceive that railroads undertake more preventive effort than they really do. In other words, customers think that railroads are safer than they are in reality. Conversely, a value of a less than one means that customers underestimate the preventive efforts of railroads and think that railroads are less safe than they are in reality. 

When customers are perfectly informed, and a equals one, this decision rule is identical to the first-order condition (equation 11.6) in the benchmark model. The benchmark level of preventive effort will be provided. However, if a is greater... 

Conversely, a value of a of less than one shifts the marginal willingness-to-pay function with respect to safety downward, and for an unchanged level of output, less preventive effort will be undertaken than in the benchmark model (Spence, 1977). A belief by customers that railroads are less safe than they really are motivates the railroad to provide less safety. In the extreme if or equals zero, meaning that customers cannot form any perception about the amount of prevention, the railroad will not take any preventive efforts because customers will be unwilling to pay the higher price that it would entail. 

If a is greater than one, and hence x is greater than x, the cost function will shift upward because the monopolist is now producing a safer service. The equilibrium level of output will be smaller than in the benchmark model. The converse conclusion will be drawn if the value of a is less than one. 

The benchmark model requires the railroad to be legally liable to compensate bystanders for harm caused by railroad accidents. The market failure, when this does not occur can be easily shown. Absent compensation, the social-welfare maximizing monopolist will set the level of preventive effort using the rule ... 

The marginal cost of preventive effort is greater than in the benchmark model. This is because the railroad no longer bears the negative marginal cost of compensation to bystanders. This marginal function is negative because an increase in preventive efforts will reduce the number of accidents and hence the compensation payments to bystanders. Consequently, for a constant level of output, the railroad will undersupply preventive effort. 

Compared with the benchmark model, the railroad will charge a lower price because it does not have to pay out compensation to bystanders. As a result, customers will purchase too much output. Bystanders therefore suffer double harm. Railroads provide less-safe service and bystanders have an increased exposure to the risk. 

If railroads are subject to strict liability to bystanders then the benchmark model would apply. This optimal result will not necessarily occur under a regime of negligence. Courts will define due care as consistent with the social>welfare maximizing level of preventive effort x). If the railroad provides this level of preventive effort or a higher level it will not be liable to compensate third parties. If it provides less preventive effort it will be liable. Therefore, the decision rule on the level of preventive effort is ... 

Railroads carry many different commodities. Most are very benign and can be cleaned up quite easily, but others cause considerable damage and are difficult to clean up. Therefore in the benchmark model, the e(x) function will vary depending on the product transported. Indicating individual products by the superscript k, the social-welfare maximizing monopoly railroad should set output on the basis of ... 

Analytical benchmark exercises focusing on the validation of computer codes used to assess the consequences of a primary coolant pipe rupture. The benchmark model would be a reference pool type LMFBR design. The objective includes studying the sensitivity of certain input parameters. 

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