Hydration of synthetic polydialkylphosphate (PPF) ? a simplified model for natural teichoic acids

A simplified model of Darwinian evolution at the molecular level is studied by applying the methods of artificial chemistry. A chemical reactor (chemostat) contains molecules that are represented by binary strings, the strings being capable of replication with a probability proportional to their fitness. Moreover, the process of replication is not fully precise, sporadic mutations may produce new offspring strings, which are slightly different from their parent templates. The dynamics of such an autoreplicating system is described by Eigen's differential equations. These equations have a unique asymptotically stable state, which corresponds to those strings that have the highest rate constants (fitness). Fitness of binary string is calculated as a graph-theory similarity between a folding (phenotype) of respective string and the so-called required folding. The presented method offers a detailed view of mechanisms of the molecular Darwinian evolution, in particular of the meaning and importance of neutral mutations.

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Crystal Forms of Semisynthetic Ergot Alkaloid Terguride

Collection of Czechoslovak Chemical Communications ◽

10.1135/cccc20020479 ◽

2002 ◽

Vol 67 (4) ◽

pp. 479-489 ◽

Cited By ~ 4

Author(s):

Michal Hušák ◽

Bohumil Kratochvíl ◽

Ivana Císařová ◽

Ladislav Cvak ◽

Alexandr Jegorov ◽

...

Keyword(s):

Crystal Structure ◽

Ergot Alkaloid ◽

Simplified Model ◽

Quantum Mechanical ◽

Quantum Mechanical Calculations ◽

X Ray Diffraction ◽

Torsion Angles ◽

Crystal Forms ◽

X Ray ◽

Independent Molecules

Two new structures of semisynthetic ergot alkaloid terguride created by unusual number of symmetry-independent molecules were determined by X-ray diffraction methods at 150 K. Form A (monoclinic, P212121, Z = 12) contains three symmetry-independent terguride molecules and two molecules of water in the asymmetric part of the unit cell. The form CA (monoclinic, P21, Z = 8) is an anhydrate remarkable by the presence of four symmetry-independent molecules in the crystal structure. Conformations of twelve symmetry-independent molecules that were found in four already described terguride structures are compared with torsion angles obtained by ab initio quantum-mechanical calculations for the simplified model of N-cyclohexyl-N'-diethylurea.

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M-groupoid as a tool for investigating mathematical models of computers

Fundamenta Informaticae ◽

10.3233/fi-1977-1107 ◽

1977 ◽

Vol 1 (1) ◽

pp. 71-91

Author(s):

Jerzy Tiuryn

Keyword(s):

Mathematical Models ◽

Simple Approximation ◽

Simplified Model ◽

Suitable Choice ◽

Iterative Systems

An M-groupoid is a simplified model of computer. The classes of M-groupoids, address machines, stored program computers and iterative systems are presented as categories – by a suitable choice of homomorphisms. It is shown that the first three categories are equivalent, whereas the fourth is weaker (it is not equivalent to the previous ones and it can easily be embedded in the category of M-groupoids). This fact proves that M-groupoids form an essentially better and reasonably simple approximation of more complicated models of computers than iterative systems.

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On the origin of long-lived particles

Journal of High Energy Physics ◽

10.1007/jhep12(2020)061 ◽

2020 ◽

Vol 2020 (12) ◽

Author(s):

Jared Barron ◽

David Curtin

Keyword(s):

Decay Mode ◽

Large Volume ◽

Simplified Model ◽

Production Mode ◽

Decay Products ◽

Bsm Physics ◽

Level 1 ◽

Displaced Vertex ◽

Main Detector ◽

Combining Information

Abstract MATHUSLA is a proposed large-volume displaced vertex (DV) detector, situated on the surface above CMS and designed to search for long-lived particles (LLPs) produced at the HL-LHC. We show that a discovery of LLPs at MATHUSLA would not only prove the existence of BSM physics, it would also uncover the theoretical origin of the LLPs, despite the fact that MATHUSLA gathers no energy or momentum information on the LLP decay products. Our analysis is simple and robust, making it easily generalizable to include more complex LLP scenarios, and our methods are applicable to LLP decays discovered in ATLAS, CMS, LHCb, or other external detectors. In the event of an LLP detection, MATHUSLA can act as a Level-1 trigger for the main detector, guaranteeing that the LLP production event is read out at CMS. We perform an LLP simplified model analysis to show that combining information from the MATHUSLA and CMS detectors would allow the LLP production mode topology to be determined with as few as ∼ 100 observed LLP decays. Underlying theory parameters, like the LLP and parent particle masses, can also be measured with ≲ 10% precision. Together with information on the LLP decay mode from the geometric properties of the observed DV, it is clear that MATHUSLA and CMS together will be able to characterize any newly discovered physics in great detail.

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Simplified Mathematical Modelling of Uncertainty: Cost-Effectiveness of COVID-19 Vaccines in Spain

Mathematics ◽

10.3390/math9050566 ◽

2021 ◽

Vol 9 (5) ◽

pp. 566

Author(s):

Julio Emilio Marco-Franco ◽

Pedro Pita-Barros ◽

Silvia González-de-Julián ◽

Iryna Sabat ◽

David Vivas-Consuelo

Keyword(s):

Cost Effectiveness ◽

Health Planning ◽

Cost Effective ◽

Incremental Cost Effectiveness Ratio ◽

Reliable Data ◽

Simplified Model ◽

Fatality Rate ◽

Cost Effectiveness Ratio ◽

Funeral Homes ◽

The Cost

When exceptional situations, such as the COVID-19 pandemic, arise and reliable data is not available at decision-making times, estimation using mathematical models can provide a reasonable reckoning for health planning. We present a simplified model (static but with two-time references) for estimating the cost-effectiveness of the COVID-19 vaccine. A simplified model provides a quick assessment of the upper bound of cost-effectiveness, as we illustrate with data from Spain, and allows for easy comparisons between countries. It may also provide useful comparisons among different vaccines at the marketplace, from the perspective of the buyer. From the analysis of this information, key epidemiological figures, and costs of the disease for Spain have been estimated, based on mortality. The fatality rate is robust data that can alternatively be obtained from death registers, funeral homes, cemeteries, and crematoria. Our model estimates the incremental cost-effectiveness ratio (ICER) to be 5132 € (4926–5276) as of 17 February 2021, based on the following assumptions/inputs: An estimated cost of 30 euros per dose (plus transport, storing, and administration), two doses per person, efficacy of 70% and coverage of 70% of the population. Even considering the possibility of some bias, this simplified model provides confirmation that vaccination against COVID-19 is highly cost-effective.

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