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can then be designed with conducting sections Molecular RTDs operating at room temperature have been demonstrated Mitre Corporation has also investigated possible architectures using organic molecules A number of designs have been advanced based on diode logic using the Tour wires and diodes AND, OR, and XOR gate designs have been shown, along with an adder The major problem with such organic systems is that the conductivity is relatively poor through the interconnecting Tour wires (the RC time constants of most of the devices is likely to be relatively large, and, unless better conductors or architectures for which the performance does not depend on resistance can be found, the organic systems will always be much slower than silicon) To be able to utilize molecules in future electronics, entire structures will have to be scaled down, including the wires connecting each component Therefore, it is essential to develop molecular wires.

from a random uniform distribution on [0 : 1] The hit-and-run distribution needs to generate uniformly (typically) on the J -dimensional unit hypersphere and a signed distance from some speci ed density (often gamma) and from a random uniform distribution on [0 :1] The Gibbs sampler only needs to generate values from conditional distributions on each step, but there must be J values generated for a 1 J coef cient vector at each step Therefore, random number generation is a key component of MCMC algorithms Random number generation is an important but understudied aspect of applied statistical computing, at least at the high end of implementation complexity (Marsaglia 1985), including Markov chain Monte Carlo implementations.

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An interesting group of molecules are the ones that consist of chains of aromatic benzene rings, such as polyphenylenes, polyporphyrines, and polythiophenes Several researchers have shown that molecules of this type conduct current and that they are capable of switching small currents [407, 408] Aromatic-based molecules bonded with multiply bonded groups (such as ethenyl, HC CH , or ethynyl, C C ) are also conductive Because of this capability, triply bonded ethynyl or acetylenic linkages can be inserted as spacers between rings in the Tour wire; spacers are needed to eliminate steric interference that can a ect the extent of p-orbital overlap between neighboring rings, thereby reducing conductiveness [237] Carbon nanotubes (discussed in 4) have also been used to conduct electrons and demonstrate reasonable conductivities for their size Both SWNTs and MWNTs can be created that may potentially reduce resistance.

Conductivities as high as 2000 Sm 1, which corresponds to a resistance of 200 / m, have been measured, substantially better than organic molecules A transistor has been demonstrated, although the gate was a silicon substrate and the carbon nanotube had been placed across two metal electrodes fabricated on top of the thermally oxidized silicon substrate Metal-nanotube recti ers have also been demonstrated To date, no switch or three-terminal devices have been produced, which are basic requirements for most logical architectures Some researchers have demonstrated measurements on nanocrystals; for example, CdSe nanocrystals can be prepared with sizes down to about 2 nm and with attached linker molecules that may bind to numerous surfaces, including gold A singleelectron transistor has been demonstrated where an oxidized silicon substrate is used as a gate to a CdSe nanocrystal placed between two gold electrodes on the SiO2 surface.

We know from a vast foundational literature that serious problems can be caused by poorly written algorithms: Good (1957), Butcher (1961), Kronmal (1964), Coveyou and MacPherson (1967), Downham and Roberts (1967), Gorenstein (1967), Marsaglia (1968), Whittlesey (1969), Downham (1970), Toothill et al (1971), Learmonth and Lewis (1973), Dieter (1975), Dudewicz (1975, 1976), McArdle (1976), Atkinson (1980), Morgan (1984), Krawczyk (1992), Gentle (1998), McCullough (1999a), and McCullough and Wilson (1999) In much the same way that the famously awed but widely used RANDU algorithm from IBM was used for quite some time although it had received quite a lot of criticism in this literature (Coveyou 1960; Fishman and Moore 1982; Hellekalek 1998), it can also be dif cult to generate random numbers with specialized non-random properties such as speci ed correlations (Hurst and Knop 1972; Kennedy and Gentle 1980; Gentle 1990; Anderson and Louis 1996; Malov 1998; Falk 1999).

There have also been e orts at measuring and achieving conductivity in di erent types of DNA Results range from highly insulating behavior to semiconducting and even to metallic behavior The best results to date correspond to Pd nanoparticles attached to a DNA strand that has demonstrated a conductivity of 100 Sm 1 There are a large number of other approaches discussed in the literature To date, however, there has not been any demonstration of an all-molecular transistor or any structure with gain..

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