Modified Born-Lande Equation to calculate Lattice Energy in a theoretical approach

Defects in ionic solid are very much common, which is increased with the rise in temperature. It causes the change in the value of many physical properties and varieties of physical parameters and the Lattice Energy is one such parameter to control the physical properties of the crystals. Considering the loss of ions from lattice points as random, the examination of each of the defects individually is going to be unpredictable, thus leading to almost nonattainment of the correct crystal structure with the theoretical calculations applying for available models. Here, in this present work, we have used some statistical methods and probabilistic approximation to introduce a novel idea of calculating the Madelung constant, and then Lattice Energy analytically. To make the understanding more lucid, we have taken one of the very common crystals, very popular in the crystallographic community, NaCl crystal having 6:6 co-ordination number, for which a significant number of Schottky defects are observed. During this study, we are bound to assume the random distribution of defects as Poisson distribution due to the fact that the number of defects is very less with respect to the total numbers of lattice points present in the crystal to calculate the Madelung Constant.

Approaching probabilistic and deterministic nomic truths in an inductive probabilistic way

Theories of truth approximation in terms of truthlikeness (or verisimilitude) almost always deal with (non-probabilistically) approaching deterministic truths, either actual or nomic. This paper deals first with approaching a probabilistic nomic truth, viz. a true probability distribution. It assumes a multinomial probabilistic context, hence with a lawlike true, but usually unknown, probability distribution. We will first show that this true multinomial distribution can be approached by Carnapian inductive probabilities. Next we will deal with the corresponding deterministic nomic truth, that is, the set of conceptually possible outcomes with a positive true probability. We will introduce Hintikkian inductive probabilities, based on a prior distribution over the relevant deterministic nomic theories and on conditional Carnapian inductive probabilities, and first show that they enable again probabilistic approximation of the true distribution. Finally, we will show, in terms of a kind of success theorem, based on Niiniluoto’s estimated distance from the truth, in what sense Hintikkian inductive probabilities enable the probabilistic approximation of the relevant deterministic nomic truth. In sum, the (realist) truth approximation perspective on Carnapian and Hintikkian inductive probabilities leads to the unification of the inductive probability field and the field of truth approximation.

A sequence embedding method for enzyme optimal condition analysis

Background An enzyme activity is influenced by the external environment. It is important to have an enzyme remain high activity in a specific condition. A usual way is to first determine the optimal condition of an enzyme by either the gradient test or by tertiary structure, and then to use protein engineering to mutate a wild type enzyme for a higher activity in an expected condition. Results In this paper, we investigate the optimal condition of an enzyme by directly analyzing the sequence. We propose an embedding method to represent the amino acids and the structural information as vectors in the latent space. These vectors contain information about the correlations between amino acids and sites in the aligned amino acid sequences, as well as the correlation with the optimal condition. We crawled and processed the amino acid sequences in the glycoside hydrolase GH11 family, and got 125 amino acid sequences with optimal pH condition. We used probabilistic approximation method to implement the embedding learning method on these samples. Based on these embedding vectors, we design a computational score to determine which one has a better optimal condition for two given amino acid sequences and achieves the accuracy 80% on the test proteins in the same family. We also give the mutation suggestion such that it has a higher activity in an expected environment, which is consistent with the previously professional wet experiments and analysis. Conclusion A new computational method is proposed for the sequence based on the enzyme optimal condition analysis. Compared with the traditional process that involves a lot of wet experiments and requires multiple mutations, this method can give recommendations on the direction and location of amino acid substitution with reference significance for an expected condition in an efficient and effective way.