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3. Better display image samples are obtained by processing measurement samples. Optimal estimation of the continuous signal f(x) at x depends on multiple measurement sample values in a neighborhood of x. Of course, this may mean that the resolution of the image display device should exceed the resolution of the sample data. Higher resolution on display is not uncommon, however, especially if one chooses to print the image. 4. Accurate signal interpolation from measurement samples is enabled by prior knowledge regarding the signal and the measurement system. In this case, we know that the signal is bandlimited by the optical MTF and thus expect the sampling theorem to apply. If the sampling theorem applies, Fig. 7.7 does more than smooth Fig. 7.6; it actually recovers the signal from sampling distortion. 5. It may be undesirable in terms of data and communication ef ciency to transmit a best image estimate from the image capture device. It may be more useful to record compressed sample data along with known system priors for later image estimation. 6. The process of sampled image recording and estimation is deeper and more subtle than one might rst suppose. Knowledge of the sampling period is suf cient to estimate g(x, y), but the sampling theorem itself is computationally unattractive. One expects that a balance between computational complexity and signal delity could be achieved using wavelets with compact support rather than the Shannon scaling function. One may consider how sampling systems can then be designed to match interpolation functions. 7. All of these points rely on the existence of careful and accurate models for the physical measurement process. The particular interpolation method used above, based on a nite support version of the Shannon generating function, is windowed sinc interpolation. The art of

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Petty N K, T J Evans, P C Fineran, and G P C Salmond (2007) Trends Biotechnol 25, 7 15 Raab R, G Neal, J Garret, R Grimaila, R Fusselman, and R Young (1986) J Bacteriol 167, 1035 1042 Raab R, G Neal, C Sohaskey, J Smith, and R Young (1988) J Mol Biol 199, 95 105 Ramanculov E R and R Young (2001a) Mol Microbiol 41, 575 583 Ramanculov E R and R Young (2001b) Mol Genet Genomics 265, 345 353 Ramanculov E R and R Young (2001c) Gene 265, 25 36 Savva C G, J S Dewey, J Deaton, R L White, D K Struck, A Holzenburg, and R Young (2008) Mol Microbiol 69, 784 793 Smith D L, D K Struck, J M Scholtzand, and R Young (1998) J Bacteriol 180, 2531 2540 Srividhya K V and S.

are prescribed, and we thus need to keep these slow variables at constant values We refer to a modification of the equations of motion that keep the slow variables constant as a vuriostut For a generalized canonical ensemble, we need to keep the Lagrange multipliers constant: we hence refer to a corresponding modification of the equations of motion as a multiplostut Note that keeping the Lagrange multipliers constant comes hand in hand with the preservation of the exponential form of the canonical ensemble (615) In this section, we discuss some basic ideas for the construction of variostats and multiplostats The distinction between variostats and multiplostatsis not always straightforward For example,control of the temperature in molecular dynamicscould naturally be classifiedas a multiplostat mechanism because temperatureoccurs as a Lagrange multiplier In practice, however, one often keeps the kinetic energy constant so that one actually deals with a variostat.

Krishnaswamy (2007) J Biosci 32, 79 90 Steiner M and U Bl si (1993) Mol Microbiol 8, 525 533 Tak c M, A Witte, and U Bl si (2005) Microbiology 151, 2331 2342 Tran T A T, D K Struck, and R Young (2005) J Bacteriol 187, 6631 6640 Wang I N, D L Smith, and R Young (2000) Annu Rev Microbiol 54, 799 825 Xu M, D K Struck, J Deaton, I N Wang, and R Young (2004) Proc Natl Acad Sci USA 101, 6415 6420 Xu M, A Arulandu, D K Struck, S Swanson, J C Sacchettini, and R Young (2005) Science 307, 113 117 Young R (1992) Microbiol Rev 56, 430 481 Young R J (2002) Mol Microbiol Biotechnol 4, 21 36 Young R and U Bl si (1995) FEMS Microbiol Rev 17, 191 205 Young R, I N.

Bulleting your points Dreamweaver Technique: adding Unordered Lists Using a numbered list Dreamweaver Technique: Inserting Ordered Lists applying Css to lists Dreamweaver Technique: applying Definition Lists Building a glossary Inserting menu and directory lists

The same situation occurs when one keeps the pressure (as another Lagrange multiplier) constant by actually fixing the value of its virial expression Of course, the subsequentlydescribed ideas for constructing variostats and multiplostats need to be combined if one uses mixed ensembles We first consider variostats To keep an observable n ( z ) constant, we modify Hamilton's equations of motion (61) for z = ( T I ,PI,,T N ,p ~as ) . follows:48 (8108) By means of the chain rule, we then obtain for rate of change of II under the variostatted time evolution (8108) rm - an _ - - - dz = 0 (8109) dt 3, dt Note that (an/az) Lo (&To/&) is the rate of change of II under Hamilton's equations of motion, which is assumed to be small for a relevant slow variable.

Wang, and W D Roof (2000) Trends Microbiol 8, 120 128 Zagotta M T and D B Wilson (1990) J Bacteriol 172, 912 921..

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