Convergence of the Gutt Star Product

In this work we consider the Gutt star product viewed as an associative deformation of the symmetric algebra S^\bullet(g) over a Lie algebra g and discuss its continuity properties: we establish a locally convex topology on S^\bullet(g) such that the Gutt star product becomes continuous. Here we have to assume a mild technical condition on g: it has to be an Asymptotic Estimate Lie algebra. This condition is e.g. fulfilled automatically for all finite-dimensional Lie algebras. The resulting completion of the symmetric algebra can be described explicitly and yields not only a locally convex algebra but also the Hopf algebra structure maps inherited from the universal enveloping algebra are continuous. We show that all Hopf algebra structure maps depend analytically on the deformation parameter. The construction enjoys good functorial properties.Comment: 35 pages, minor typos corrected, updated bibliograph

Educational situation of teaching Polish language in Norway

Poles are the largest group of immigrants living in Norway. Deeper penetration into the structure of society of the Polish people will diagnose its current needs and anticipate their future requirements. This raises the need for a variety of interdisciplinary research on the problems of migration, as well as analyses of cultural studies, sociology, linguistics, cultural psychology. At the moment the most urgent is educational aspect. The high increase of births of Polish children can predict that in a few years Norway will face an even greater challenge than today. That is why it is significantly important to take care of the development of Polish schools abroad and strive for its popularization. This article shows the educational situation of teaching Polish language in Norway. Author presented history of teaching native languages in Norway, the way of organizing teaching Polish as a mother tongue and types of activities. Polonial education in the Kingdom was characterized from different perspectives: profile of pupils and teachers, teaching materials, demand. (У статті описується ситуація польської мови у Норвегії. Представлено історію викладання рідних мов у Норвегії, спосіб існування польської мови як рідної та види занять. Суботні польські школи охарактеризовано з різних аспектів, а саме учнів, викладачів, матеріалів викладання, потреб. У статті представлено діяльність та специфіку найстаршої польської школи у Норвегії.

Model of early stage intermediate in respect to its final structure

The model, describing a method of determining the structure of an early intermediate in the process of protein folding to analyze nonredundant PDB protein bases, allows determining the relationship between the sequence of tetrapeptides and their structural forms expressed by structural codes. The contingency table expressing such a relationship can be used to predict the structure of polypeptides by proposing a structural form with a precision limited to the structural code. However, by analyzing structural forms in native forms of proteins based on the fuzzy oil drop model, one can also determine the status of polypeptide chain fragments with respect to the assumptions of this model. Whether the probability distributions for both compliant and noncompliant forms were similar or whether the tetrapeptide sequences showed some differences at a level of a set of structural codes was investigated. The analysis presented here indicated that some sequences in both forms revealed differences in probability distributions expressed as a negative statistically significant correlation coefficient. This meant that the identified sections (tetrapeptides) took different forms against the fuzzy oil drop model. It may suggest that the information of the final status with respect to hydrophobic core formation is already carried by the structure of the early-stage intermediate

Ultrasonographic caval indices do not significantly contribute to predicting fluid responsiveness immediately after coronary artery bypass grafting when compared to passive leg raising

IVC_PLR_dataset (XLSX 15 kb

Structure of the hydrophobic core determines the 3D protein structure-verification by single mutation proteins

Four de novo proteins differing in single mutation positions, with a chain length of 56 amino acids, represent diverse 3D structures: monomeric 3$\alpha$ and 4$\beta$ + $\alpha$ folds. The reason for this diversity is seen in the different structure of the hydrophobic core as a result of synergy leading to the generation of a system in which the polypeptide chain as a whole participates. On the basis of the fuzzy oil drop model, where the structure of the hydrophobic core is expressed by means of the hydrophobic distribution function in the form of a 3D Gaussian distribution, it has been shown that the composition of the hydrophobic core in these two structural forms is different. In addition, the use of a model to determine the structure of the early intermediate in the folding process allows to indicate differences in the polypeptide chain geometry, which, combined with the construction of a common hydrophobic nucleus as an effect of specific synergy, may indicate the reason for the diversity of the folding process of the polypeptide chain. The results indicate the need to take into account the presence of an external force field originating from the water environment and that its active impact on the formation of a hydrophobic core whose participation in the stabilization of the tertiary structure is fundamental

Machine Learning and EEG for Emotional State Estimation

Defining “emotion” and its accurate measuring is a notorious problem in the psychology domain. It is usually addressed with subjective self-assessment forms filled manually by participants. Machine learning methods and EEG correlates of emotions enable to construction of automatic systems for objective emotion recognition. Such systems could help to assess emotional states and could be used to improve emotional perception. In this chapter, we present a computer system that can automatically recognize an emotional state of a human, based on EEG signals induced by a standardized affective picture database. Based on the EEG signal, trained deep neural networks are then used together with mappings between emotion models to predict the emotions perceived by the participant. This, in turn, can be used for example in validation of affective picture databases standardization

Divergence entropy-based evaluation of hydrophobic core in aggressive and resistant forms of transthyretin

The two forms of transthyretin differing slightly in the tertiary structure, despite the presence of five mutations, show radically different properties in terms of susceptibility to the amyloid transformation process. These two forms of transthyretin are the object of analysis. The search for the sources of these differences was carried out by means of a comparative analysis of the structure of these molecules in their native and early intermediate stage forms in the folding process. The criterion for assessing the degree of similarity and differences is the status of the hydrophobic core. The comparison of the level of arrangement of the hydrophobic core and its initial stages is possible thanks to the application of divergence entropy for the early intermediate stage and for the final forms. It was shown that the minimal differences observed in the structure of the hydrophobic core of the forms available in PDB, turned out to be significantly different in the early stage (ES) structure in folding process. The determined values of divergence entropy for both ES forms indicate the presence of the seed of hydrophobic core only in the form resistant to amyloid transformation. In the form of aggressively undergoing amyloid transformation, the structure lacking such a seed is revealed, being a stretched one with a high content of β-type structure. In the discussed case, the active presence of water in the structural transformation of proteins expressed in the fuzzy oil drop model (FOD) is of decisive importance for the generation of the final protein structure. It has been shown that the resistant form tends to generate a centric hydrophobic core with the possibility of creating a globular structure, i.e., a spherical micelle-like form. The aggressively transforming form reveals in the structure of its early intermediate, a tendency to form the ribbon-like micelle as observed in amyloid

Engagement of intrinsic disordered proteins in protein–protein interaction

Proteins from the intrinsically disordered group (IDP) focus the attention of many researchers engaged in protein structure analysis. The main criteria used in their identification are lack of secondary structure and significant structural variability. This variability takes forms that cannot be identified in the X-ray technique. In the present study, different criteria were used to assess the status of IDP proteins and their fragments recognized as intrinsically disordered regions (IDRs). The status of the hydrophobic core in proteins identified as IDPs and in their complexes was assessed. The status of IDRs as components of the ordering structure resulting from the construction of the hydrophobic core was also assessed. The hydrophobic core is understood as a structure encompassing the entire molecule in the form of a centrally located high concentration of hydrophobicity and a shell with a gradually decreasing level of hydrophobicity until it reaches a level close to zero on the protein surface. It is a model assuming that the protein folding process follows a micellization pattern aiming at exposing polar residues on the surface, with the simultaneous isolation of hydrophobic amino acids from the polar aquatic environment. The use of the model of hydrophobicity distribution in proteins in the form of the 3D Gaussian distribution described on the protein particle introduces the possibility of assessing the degree of similarity to the assumed micelle-like distribution and also enables the identification of deviations and mismatch between the actual distribution and the idealized distribution. The FOD (fuzzy oil drop) model and its modified FOD-M version allow for the quantitative assessment of these differences and the assessment of the relationship of these areas to the protein function. In the present work, the sections of IDRs in protein complexes classified as IDPs are analyzed. The classification “disordered” in the structural sense (lack of secondary structure or high flexibility) does not always entail a mismatch with the structure of the hydrophobic core. Particularly, the interface area, often consisting of IDRs, in many analyzed complexes shows the compliance of the hydrophobicity distribution with the idealized distribution, which proves that matching to the structure of the hydrophobic core does not require secondary structure ordering

Different synergy in amyloids and biologically active forms of proteins

Protein structure is the result of the high synergy of all amino acids present in the protein. This synergy is the result of an overall strategy for adapting a specific protein structure. It is a compromise between two trends: The optimization of non-binding interactions and the directing of the folding process by an external force field, whose source is the water environment. The geometric parameters of the structural form of the polypeptide chain in the form of a local radius of curvature that is dependent on the orientation of adjacent peptide bond planes (result of the respective Phi and Psi rotation) allow for a comparative analysis of protein structures. Certain levels of their geometry are the criteria for comparison. In particular, they can be used to assess the differences between the structural form of biologically active proteins and their amyloid forms. On the other hand, the application of the fuzzy oil drop model allows the assessment of the role of amino acids in the construction of tertiary structure through their participation in the construction of a hydrophobic core. The combination of these two models-the geometric structure of the backbone and the determining of the participation in the construction of the tertiary structure that is applied for the comparative analysis of biologically active and amyloid forms - is presented