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Toward Understanding the Intelligent Properties of Biological Macromolecules
Published in George K. Knopf, Amarjeet S. Bassi, Smart Biosensor Technology, 2018
These results support the validity of our approach using the PD scale parameters to begin to understand the energetic basis of DNA sequences interacting with their recognition proteins. One advantage this approach provides is that DNA sequence-based physical properties are far easier to calculate than protein physical properties. This results from the fact that all DNA as it occurs inside cells has a regular repeating secondary structure close to the B secondary structure proposed originally by Watson and Crick (171). As a consequence, a number of different dinucleotide- and trinucleotide-based DNA physical property data sets (PD, bendability, and position preference) have been calculated from experimental data (172). Using these data sets, the local physical properties for any DNA sequence can be calculated. No such equivalent simple computational rules exist for proteins, which lack the overall energetic and structural uniformity that DNA possesses. The computational approach we have described has important implications for the use of DNA–protein complexes in biosensors. Stability and property differences for DNA sequence variants of DNA–protein complexes may eventually be predictable through simple calculations. This would be a valuable capability, since the laborious experimental generation of altered DNA sequences and testing of their DNA–protein stabilities and properties would not need to be performed prior to their use in biosensors.
Single-System Performance and Sensitivity
Published in Chia-Chi Tsui, Robust Control System Design, 2022
Figure 2.2 shows that as the frequency ω increases from 0 to infinity, the function |G(jω)| starts at 1 and eventually decays to 0. BW is defined as the frequency at which |G(jω)| reaches 1/√2 ≈ 0.707. Figure 2.2 shows that (Chen, 1993) BW≈1.6ωnto0.6ωn,whenζisfrom0.1to1
Medical Decision Making
Published in Pat Croskerry, Karen S. Cosby, Mark L. Graber, Hardeep Singh, Diagnosis, 2017
The calculation of mathematical probabilities and the use of Bayesian analysis (or perhaps more appropriately, Bayesian inference) lends an aura of certainty to diagnostic reasoning, but we must be cautious in how much trust we place in the results. Posttest probability is predicated on pretest probability, which in turn, is determined by clinical judgment, or expert opinion—or put another way, an educated guess. And while one might think that these methods should reduce uncertainty and be met with enthusiasm, in fact, most clinicians don’t have a working understanding of many of these statistical concepts, and even fewer use them at the bedside [42,43]. Studies of actual clinician performance demonstrated that most do poorly in their estimates of probability of disease [44], and there is significant interobserver variation in estimation of risk [45]. The accuracy of clinical judgment varies so much between individuals that one can question whether there is anything of value added in all this analysis, something that is explored more in Chapter 9 (Individual Variability in Clinical Decision Making and Diagnosis). That does not necessarily mean that statistical methods don’t influence and improve care. The mathematical analysis of risk and probability factors into clinical decision rules and eventually affects standard of practice. In any given moment at the bedside, clinicians may not form questions, search data sets, or calculate odds, but they are likely familiar with evolving practice guidelines that are heavily influenced by these methods. Clinicians who actively seek feedback can hope to outperform the norm, but they need a supportive environment and tools to optimize their calibration and decision making [46,47].
Strong convergence of two regularized relaxed extragradient schemes for solving the split feasibility and fixed point problem with multiple output sets
Published in Applicable Analysis, 2023
Adeolu Taiwo, Simeon Reich, Chinedu Izuchukwu
Case I: Suppose that the sequence is eventually decreasing, that is, there exists a natural number such that is decreasing for . Since is bounded, this implies that it is convergent. Therefore, taking the limit in (29) as and using the conditions imposed on the control sequences, we see that and Now, using (32), we get Using (32) and (33), we obtain and using (15) and (36), we get Also, from (15) and (35), it follows that Using (34), (38) and (39), we now obtain that .
Eigenfunctions of the Perron–Frobenius operators for generalized beta-maps
Published in Dynamical Systems, 2022
The lap-counting function converges absolutely in the open disk . In addition, for with , we have where , regard as if there is no positive integer n such that , and we regard as 0 if . Therefore, can be extended to the meromorphic function in the unit open disc. In particular, if the coefficient sequence is eventually periodic, then can be extended to a rational function. Otherwise cannot be extended to a meromorphic function beyond the unit circle. Furthermore, has a simple pole at .
An iterative viscosity approximation method for the split common fixed-point problem
Published in Optimization, 2021
Huimin He, Jigen Peng, Qinwei Fan
Case II: The sequence is not eventually nonincreasing at infinity. In this case, we have a subsequence such that for all . Hence, we can use Lemma 2.3 to construct a subsequence , with such that for all .