Polytopic Prismahedrons

The structure of polytopes—polytopic prismahedrons, which are products of polytopes of lower dimensionality—is investigated. The products of polytopes do not belong to the well-studied class of simplicial polytopes, and therefore their investigations are of independent interest. Analytical dependencies characterizing the structure of the product of polytopes are obtained as a function of the structures of polytope factors. Images of a number of specific polytopic prismahedrons are obtained, tables of structures of polytopic prismahedrons are compiled, depending on the types of polytopes of the factors. Polytopic prismahedrons can be considered as a result of the chemical interaction of molecules, which, from among which there is a polytope of a certain dimension.

The structure of polytopes - polytopic prismahedrons, which are products of polytopes of lower dimensionality, is investigated. The products of polytopes do not belong to the well-studied class of simplicial polytopes, and therefore their investigations are of independent interest. Analytical dependencies characterizing the structure of the product of polytopes are obtained as a function of the structures of polytope factors. Images of a number of specific polytopic prismahedrons are obtained, tables of structures of polytopic prismahedrons are compiled, depending on the types of polytopes of the factors. The geometric properties of the boundary complexes of polytopic prismehedrons are investigated. Polytopic prismahedrons can be considered as a result of the chemical interaction of molecules, which, from among which there is a polytope of a certain dimension. The possibility of the multivaluedness of the incidence coefficients of geometric elements of polytopic prisms is revealed. It is shown that polytopic prismahedra, due to their nature, as products of polytopes, ensure the filling of n-dimensional spaces during their translation, creating a structure similar to the structure of quasicrystals.


2019 ◽  
Vol 72 (2) ◽  
pp. 537-556
Author(s):  
Eran Nevo ◽  
Guillermo Pineda-Villavicencio ◽  
Julien Ugon ◽  
David Yost

AbstractWe study $n$-vertex $d$-dimensional polytopes with at most one nonsimplex facet with, say, $d+s$ vertices, called almost simplicial polytopes. We provide tight lower and upper bound theorems for these polytopes as functions of $d,n$, and $s$, thus generalizing the classical Lower Bound Theorem by Barnette and the Upper Bound Theorem by McMullen, which treat the case where $s=0$. We characterize the minimizers and provide examples of maximizers for any $d$. Our construction of maximizers is a generalization of cyclic polytopes, based on a suitable variation of the moment curve, and is of independent interest.


The structure of polytopes of higher dimension (polytopic prismahedrons), which are products of polytopes of lower dimensionality, is investigated. The products of polytopes do not belong to the well-studied class of simplicial polytopes, and therefore, their investigations are of independent interest. Analytical dependencies characterizing the structure of the product of polytopes are obtained as a function of the structures of polytope factors. Images of a number of specific polytopic prismahedrons are obtained, and tables of structures of polytopic prismahedrons are compiled depending on the types of polytopes of the factors. The geometric properties of the boundary complexes of polytopic prismahedrons are investigated.


2020 ◽  
Vol 17 (2) ◽  
pp. 256-277
Author(s):  
Ol'ga Veselovska ◽  
Veronika Dostoina

For the derivatives of Chebyshev second-kind polynomials of a complex vafiable, a system of functions biorthogonal with them on closed curves of the complex plane is constructed. Properties of these functions and the conditions of expansion of analytic functions in series in polynomials under consideration are established. The examples of such expansions are given. In addition, we obtain some combinatorial identities of independent interest.


Author(s):  
Prakash Goudanavar ◽  
Ankit Acharya ◽  
Vinay C.H

Administration of an antiviral drug, acyclovir via the oral route leads to low and variable bioavailability (15-30%). Therefore, this research work was aimed to enhance bioavailability of acyclovir by nanocrystallization technique. The drug nanocrystals were prepared by anti-solvent precipitation method in which different stabilizers were used. The formed nanocrystals are subjected to biopharmaceutical characterization including solubility, particle size and in-vitro release. SEM studies showed nano-crystals were crystalline nature with sharp peaks. The formulated drug nanocrystals were found to be in the range of 600-900nm and formulations NC7 and NC8 showed marked improvement in dissolution velocity when compared to pure drug, thus providing greater bioavailability. FT-IR and DSC studies revealed the absence of any chemical interaction between drug and polymers used. 


2020 ◽  
Author(s):  
Xiang Liu ◽  
Luca Capriotti ◽  
Tiankai Yao ◽  
Jason Harp ◽  
Michael T. Benson ◽  
...  

2019 ◽  
Vol 24 (34) ◽  
pp. 4007-4012 ◽  
Author(s):  
Alessandra Lumini ◽  
Loris Nanni

Background: Anatomical Therapeutic Chemical (ATC) classification of unknown compound has raised high significance for both drug development and basic research. The ATC system is a multi-label classification system proposed by the World Health Organization (WHO), which categorizes drugs into classes according to their therapeutic effects and characteristics. This system comprises five levels and includes several classes in each level; the first level includes 14 main overlapping classes. The ATC classification system simultaneously considers anatomical distribution, therapeutic effects, and chemical characteristics, the prediction for an unknown compound of its ATC classes is an essential problem, since such a prediction could be used to deduce not only a compound’s possible active ingredients but also its therapeutic, pharmacological, and chemical properties. Nevertheless, the problem of automatic prediction is very challenging due to the high variability of the samples and the presence of overlapping among classes, resulting in multiple predictions and making machine learning extremely difficult. Methods: In this paper, we propose a multi-label classifier system based on deep learned features to infer the ATC classification. The system is based on a 2D representation of the samples: first a 1D feature vector is obtained extracting information about a compound’s chemical-chemical interaction and its structural and fingerprint similarities to other compounds belonging to the different ATC classes, then the original 1D feature vector is reshaped to obtain a 2D matrix representation of the compound. Finally, a convolutional neural network (CNN) is trained and used as a feature extractor. Two general purpose classifiers designed for multi-label classification are trained using the deep learned features and resulting scores are fused by the average rule. Results: Experimental evaluation based on rigorous cross-validation demonstrates the superior prediction quality of this method compared to other state-of-the-art approaches developed for this problem. Conclusion: Extensive experiments demonstrate that the new predictor, based on CNN, outperforms other existing predictors in the literature in almost all the five metrics used to examine the performance for multi-label systems, particularly in the “absolute true” rate and the “absolute false” rate, the two most significant indexes. Matlab code will be available at https://github.com/LorisNanni.


2020 ◽  
Vol 17 (4) ◽  
pp. 498-506 ◽  
Author(s):  
Pavan K. Mujawdiya ◽  
Suman Kapur

: Quorum Sensing (QS) is a phenomenon in which bacterial cells communicate with each other with the help of several low molecular weight compounds. QS is largely dependent on population density, and it triggers when the concentration of quorum sensing molecules accumulate in the environment and crosses a particular threshold. Once a certain population density is achieved and the concentration of molecules crosses a threshold, the bacterial cells show a collective behavior in response to various chemical stimuli referred to as “auto-inducers”. The QS signaling is crucial for several phenotypic characteristics responsible for bacterial survival such as motility, virulence, and biofilm formation. Biofilm formation is also responsible for making bacterial cells resistant to antibiotics. : The human gut is home to trillions of bacterial cells collectively called “gut microbiota” or “gut microbes”. Gut microbes are a consortium of more than 15,000 bacterial species and play a very crucial role in several body functions such as metabolism, development and maturation of the immune system, and the synthesis of several essential vitamins. Due to its critical role in shaping human survival and its modulating impact on body metabolisms, the gut microbial community has been referred to as “the forgotten organ” by O`Hara et al. (2006) [1]. Several studies have demonstrated that chemical interaction between the members of bacterial cells in the gut is responsible for shaping the overall microbial community. : Recent advances in phytochemical research have generated a lot of interest in finding new, effective, and safer alternatives to modern chemical-based medicines. In the context of antimicrobial research various plant extracts have been identified with Quorum Sensing Inhibitory (QSI) activities among bacterial cells. This review focuses on the mechanism of quorum sensing and quorum sensing inhibitors isolated from natural sources.


Author(s):  
Olivia Caramello

This chapter develops a general theory of extensions of flat functors along geometric morphisms of toposes; the attention is focused in particular on geometric morphisms between presheaf toposes induced by embeddings of categories and on geometric morphisms to the classifying topos of a geometric theory induced by a small category of set-based models of the latter. A number of general results of independent interest are established on the way, including developments on colimits of internal diagrams in toposes and a way of representing flat functors by using a suitable internalized version of the Yoneda lemma. These general results will be instrumental for establishing in Chapter 6 the main theorem characterizing the class of geometric theories classified by a presheaf topos and for applying it.


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