Synthesis of four new neuro-statistical tests for testing the hypothesis of independence of small samples of biometric data

The paper considers the analysis of small samples according to several statistical criteria to test the hypothesis of independence, since the direct calculation of the correlation coefficients using the Pearson formula gives an unacceptably high error on small biometric samples. Each of the classical statistical criteria for testing the hypothesis of independence can be replaced with an equivalent artificial neuron. Neuron training is performed based on the condition of obtaining equal probabilities of errors of the first and second kind. To improve the quality of decisions made, it is necessary to use a variety of statistical criteria, both known and new. It is necessary to form networks of artificial neurons, generalizing the number of artificial neurons that is necessary for practical use. It is shown that the classical formula for calculating the correlation coefficients can be modified with four options. This allows you to create a network of 5 artificial neurons, which is not yet able to reduce the probability of errors in comparison with the classical formula. A gain in the confidence level in the future can only be obtained when using a network of more than 23 artificial neurons, if we apply the simplest code to detect and correct errors.

Global Hölder continuity of solutions to quasilinear equations with Morrey data

We deal with general quasilinear divergence-form coercive operators whose prototype is the [Formula: see text]-Laplacean operator. The nonlinear terms are given by Carathéodory functions and satisfy controlled growth structure conditions with data belonging to suitable Morrey spaces. The fairly non-regular boundary of the underlying domain is supposed to satisfy a capacity density condition which allows domains with exterior corkscrew property. We prove global boundedness and Hölder continuity up to the boundary for the weak solutions of such equations, generalizing this way the classical [Formula: see text]-result of Ladyzhenskaya and Ural’tseva to the settings of the Morrey spaces.

The combination of UHPLC-HRMS and molecular networking improving discovery efficiency of chemical components in Chinese Classical Formula

Background It is essential to identify the chemical components for the quality control methods establishment of Chinese Classical Formula (CCF). However, CCF are complex mixture of several herbal medicines with huge number of different compounds and they are not equal to the combination of chemical components from each herb due to particular formula ratio and preparation techniques. Therefore, it is time-consuming to identify compounds in a CCF by analyzing the LC–MS/MS data one by one, especially for unknown components. Methods An ultra-high pressure liquid chromatography-linear ion trap-orbitrap high resolution mass spectrometry (UHPLC-LTQ-Orbitrap-MS/MS) approach was developed to comprehensively profile and characterize multi-components in CCF with Erdong decoction composed of eight herbal medicines as an example. Then the MS data of Erdong decoction was analyzed by MS/MS-based molecular networking and these compounds with similar structures were connected to each other into a cluster in the network map. Then the unknown compounds connected to known compounds in a cluster of the network map were identified due to their similar structures. Results Based on the clusters of the molecular networking, 113 compounds were rapidly tentative identification from Erdong decoction for the first time in the negative mode, which including steroidal saponins, triterpenoid saponins, flavonoid O-glycosides and flavonoid C-glycosides. In addition, 10 alkaloids were tentatively identified in the positive mode from Nelumbinis folium by comparison with literatures. Conclusion MS/MS-based molecular networking technique is very useful for the rapid identification of components in CCF. In Erdong decoction, this method was very suitable for the identification of major steroidal saponins, triterpenoid saponins, and flavonoid C-glycosides.

Modeling of quantum-like cognitive phenomena by the Fourier-holography technique under the choice of alternatives

The article is dedicated to the search for a biologically motivated mechanism of the cognitive phenomenon of violation of the classical formula of total probability for the disjunction of incompatible events, which is considered by a number of researchers as a quantum-like phenomenon. A classical mechanism implemented by the 6f Fourier holography scheme of the resonant architecture that does not require reference to quantum mechanics either in its physical nature or at the level of formalism is demonstrated. In the analysis, the decision-making is interpreted as a choice of alternatives by using the non-cooperative game "Prisoner's Dilemma". The approach to the task is based on the search for a mechanism for forming a conditional estimate under a condition that contradicts the rule of monotonous decision logic. It is demonstrated that this estimate, in contrast to the unconditional and conditional one with a non-contradictory condition, is formed by logic with exception. The ring architecture of the holographic setup corresponds to the biologically inspired neural network concept of the excitation ring and implements cognitive dissonance on logic with exception. Conditions and ranges of violation of the classical formula of total probability in relation to the correlation radius of the reference image recorded in a hologram storing the monotone logic inference rule are analytically determined. The analytical model is confirmed by a quantitative coincidence of the results of numerical modeling with the published results of natural experiments.

The Combination of UHPLC-HRMS and Molecular Networking Improving Discovery Efficiency of Chemical Components in Chinese Classical Formula

Background It is essential to identify the chemical components for the quality control methods establishment of Chinese Classical Formula (CCF). However, CCF are complex mixture of several herbal medicines with huge number of different compounds and they are not equal to the combination of chemical components from each herb due to particular formula ratio and preparation techniques. Therefore, it is time-consuming to identify compounds in a CCF by analyzing the LC-MS/MS data one by one, especially for unknown components. Methods An ultra-high pressure liquid chromatography-linear ion trap-orbitrap high resolution mass spectrometry (UHPLC-LTQ-Orbitrap-MS/MS) approach was developed to comprehensively profile and characterize multi-components in CCF with Erdong decoction composed of eight herbal medicines as an example. Then the MS data of Erdong decoction was analyzed by MS/MS-based molecular networking and these compounds with similar structures were connected to each other into a cluster in the network map. Then the unknown compounds connected to known compounds in a cluster of the network map were identified due to their similar structures. Results Based on the clusters in the molecular networking, 113 compounds were rapidly identified from Erdong decoction for the first time, which including steroidal saponins, triterpenoid saponins, flavone O-glycosides and flavone C-glycosides. Conclusion MS/MS-based molecular networking technique is very useful for the rapid identification of components in CCF. In Erdong decoction, this method was very suitable for the identification of major steroidal saponins, triterpenoid saponins, and flavone C-glycosides.

Anti-inflammatory Properties of Fangji Huangqi Tang: Discovery Based on Network Pharmacology, Molecular Docking and Arrowsmith Tools

Fangji Huangqi Tang (FHT) is a classical formula widely used in Chinese clinical practice. In this study, a creative application of FHT for inflammation has been identified by network pharmacology-based framework. Specifically, a total of 17 bioactive compounds including 42 potential targets of FHT, and 205 related targets involved in inflammation were retrieved from mainstream databases and subjected to network analysis. 13 intersection targets indicated the principal elements linked to inflammation therapy. Top terms of Gene Ontology (GO) analysis were identified, while 7 related signaling pathways were revealed by Kyoto Encyclopedia of Genes and Genomes (KEGG) results. Subsequently, Calycosin-PTGS2 with tight binding affinity (BA) was manifested by molecular docking as the critical compound-target couple. Meaningful links between Calycosin and inflammation were implied through Arrowsmith, which overlapped with the findings in enrichment analysis, such as MAPK, NF-κB that could be regulators of PTGS2. In summary, the present study explored the potential targets and signaling pathways of FHT against inflammation, which may help to illustrate the mechanisms responsible for the action of FHT and provide a better understanding of its anti-inflammatory effects.

The Golden Rule in Thomas Reid's System of First Principles of Morality

In Modern times, the Golden Rule, the classical formula of which is contained in the Sermon on the Mount Matthew 7:12, is the subject of discussion in a number of moral and philosophical teachings as a specifically moral concept that partially or completely expresses the normative meaning of morality. It is in the Moderntimes that the rule gets its name of the Golden one. In the article, the modern understanding of the Golden Rule is considered on the basis of Thomas Reid’s ethics, who included the rule formula among the first principles of morality, i.e. self-evident principles that constitute moral thinking, determine moral reasoning, from which the entire system of moral duties is derived, and any person who seeks to understand what his duty is in specific circumstances, based on them, can do this. The main purpose of the Golden Rule, Reid saw in the fact that its application allows you to overcome the individual's partiality for himself and prejudice against others – which turns out to be destructive for human relations. He considers the Golden Rule as the rule of impartiality. The article shows that the special place that Reid assigned to the Golden Rule in the system of first principles was determined by the fact that (1) Reid described only the Golden Rule as the rule of the Divine teacher and overshadowed with the authority of the law and the prophets; (2) he described the rule as “the most comprehensive”, i.e. extending its effect to all possible relations between people – equal and unequal, including the relation of a person to himself, and all types of duties (to himself and others, perfect and imperfect). The article concludes that Reid presented the Golden Rule as an expression of the entire normative content of morality. Therefore, although he did not build a hierarchy of first principles, we can conclude that the Golden Rule by the very logic of Reid in his system turns out to be the highest.

q-Analogues of Guillera’s two series for π±2 with convergence rate 27 64

Three transformation formulae are established for the partial sum of Bailey’s well-poised [Formula: see text]-series. Their particular cases provide [Formula: see text]-analogues of Guillera’s two series for [Formula: see text] with convergence rate [Formula: see text], and for other classical [Formula: see text]-related infinite series.