scholarly journals Enumerating Tree-Like Graphs and Polymer Topologies with a Given Cycle Rank

Entropy ◽  
2020 ◽  
Vol 22 (11) ◽  
pp. 1295
Author(s):  
Naveed Ahmed Azam ◽  
Aleksandar Shurbevski ◽  
Hiroshi Nagamochi
Keyword(s):  
Chemical Compounds ◽  
Canonical Representation ◽  
Cycle Rank ◽  
Multiple Edges ◽  
Isomorphic Graphs ◽  
Important Notion

Cycle rank is an important notion that is widely used to classify, understand, and discover new chemical compounds. We propose a method to enumerate all non-isomorphic tree-like graphs of a given cycle rank with self-loops and no multiple edges. To achieve this, we develop an algorithm to enumerate all non-isomorphic rooted graphs with the required constraints. The idea of our method is to define a canonical representation of rooted graphs and enumerate all non-isomorphic graphs by generating the canonical representation of rooted graphs. An important feature of our method is that for an integer n≥1, it generates all required graphs with n vertices in O(n) time per graph and O(n) space in total, without generating invalid intermediate structures. We performed some experiments to enumerate graphs with a given cycle rank from which it is evident that our method is efficient. As an application of our method, we can generate tree-like polymer topologies of a given cycle rank with self-loops and no multiple edges.

scholarly journals An Efficient Algorithm to Count Tree-Like Graphs with a Given Number of Vertices and Self-Loops

Entropy ◽  
2020 ◽  
Vol 22 (9) ◽  
pp. 923 ◽  
Author(s):  
Naveed Ahmed Azam ◽  
Aleksandar Shurbevski ◽  
Hiroshi Nagamochi
Keyword(s):  
Dynamic Programming ◽  
Graph Theory ◽  
Lower Bound ◽  
Upper Bound ◽  
Efficient Algorithm ◽  
Rooted Tree ◽  
Chemical Compounds ◽  
Natural Sciences ◽  
Interesting Problem ◽  
Cycle Rank

Graph enumeration with given constraints is an interesting problem considered to be one of the fundamental problems in graph theory, with many applications in natural sciences and engineering such as bio-informatics and computational chemistry. For any two integers n≥1 and Δ≥0, we propose a method to count all non-isomorphic trees with n vertices, Δ self-loops, and no multi-edges based on dynamic programming. To achieve this goal, we count the number of non-isomorphic rooted trees with n vertices, Δ self-loops and no multi-edges, in O(n2(n+Δ(n+Δ·min{n,Δ}))) time and O(n2(Δ2+1)) space, since every tree can be uniquely viewed as a rooted tree by either regarding its unicentroid as the root, or in the case of bicentroid, by introducing a virtual vertex on the bicentroid and assuming the virtual vertex to be the root. By this result, we get a lower bound and an upper bound on the number of tree-like polymer topologies of chemical compounds with any “cycle rank”.

A finite graph is homeomorphic to the Reeb graph of a Morse–Bott function

2021 ◽  
Vol 71 (3) ◽  
pp. 757-772
Author(s):  
Irina Gelbukh
Keyword(s):  
Fundamental Group ◽  
Height Function ◽  
Finite Graph ◽  
Critical Values ◽  
Reeb Graph ◽  
Special Cases ◽  
Cycle Rank ◽  
Multiple Edges

Abstract We prove that a finite graph (allowing loops and multiple edges) is homeomorphic (isomorphic up to vertices of degree two) to the Reeb graph of a Morse–Bott function on a smooth closed n-manifold, for any dimension n ≥ 2. The manifold can be chosen orientable or non-orientable; we estimate the co-rank of its fundamental group (or the genus in the case of surfaces) from below in terms of the cycle rank of the graph. The function can be chosen with any number k ≥ 3 of critical values, and in a few special cases with k < 3. In the case of surfaces, the function can be chosen, except for a few special cases, as the height function associated with an immersion ℝ3.

Cytochemical analysis of mast cell granules after poly-dl-lysine action

1978 ◽  
Vol 36 (2) ◽  
pp. 278-279
Author(s):  
R. Courtoy ◽  
L.J. Simar ◽  
J. Christophe
Keyword(s):  
Mast Cell ◽  
Mast Cells ◽  
Chemical Compounds ◽  
Cellular Membrane ◽  
Thin Sections ◽  
Organic Bases ◽  
Ferric Thiocyanate ◽  
Cytochemical Analysis ◽  
Mast Cell Granule ◽  
Amine Liberation

Several chemical compounds induce amine liberation from mast cells but do not necessarily provoque the granule expulsion. For example, poly-dl-lysine induces modifications of the cellular membrane permeability which promotes ion exchange at the level of mast cell granules. Few of them are expulsed but the majority remains in the cytoplasm and appears less dense to the electrons. A cytochemical analysis has been performed to determine the composition of these granules after the polylysine action.We have previously reported that it was possible to demonstrate polyanions on epon thin sections using a cetylpyridinium ferric thiocyanate method. Organic bases are selectively stained with cobalt thiocyanate and the sulfhydryle groups are characterized with a silver methenamine reaction. These techniques permit to reveal the mast cell granule constituents, i.e. heparin, biogenic amines and basic proteins.

Growth of near noble metal Pd and Pt thin film silicides morphology and structure

1984 ◽  
Vol 42 ◽  
pp. 498-499
Author(s):  
E. I. Alessandrini ◽  
M. O. Aboelfotoh
Keyword(s):  
Noble Metals ◽  
Annealing Temperature ◽  
Chemical Compounds ◽  
Barrier Properties ◽  
Solid State Reactions ◽  
Transmission Electron ◽  
Stable Chemical ◽  
Metal Thickness ◽  
Amorphous Si ◽  
Si Films

Considerable interest has been generated in solid state reactions between thin films of near noble metals and silicon. These metals deposited on Si form numerous stable chemical compounds at low temperatures and have found applications as Schottky barrier contacts to silicon in VLSI devices. Since the very first phase that nucleates in contact with Si determines the barrier properties, the purpose of our study was to investigate the silicide formation of the near noble metals, Pd and Pt, at very thin thickness of the metal films on amorphous silicon.Films of Pd and Pt in the thickness range of 0.5nm to 20nm were made by room temperature evaporation on 40nm thick amorphous Si films, which were first deposited on 30nm thick amorphous Si3N4 membranes in a window configuration. The deposition rate was 0.1 to 0.5nm/sec and the pressure during deposition was 3 x 10 -7 Torr. The samples were annealed at temperatures in the range from 200° to 650°C in a furnace with helium purified by hot (950°C) Ti particles. Transmission electron microscopy and diffraction techniques were used to evaluate changes in structure and morphology of the phases formed as a function of metal thickness and annealing temperature.

Analysis of Bioactive Chemical Compounds of Trogoderma granarium (Insecta: Coleoptera: Dermestidae) Using Gas Chromatography – Mass Spectrometry

2017 ◽  
Vol 9 (03) ◽  
Author(s):  
Jenan Mohammed Ubaid ◽  
Abeer Fauzi Al-Rubaye ◽  
Imad Hadi Hameed
Keyword(s):  
Acetic Acid ◽  
Benzoyl Chloride ◽  
Methanolic Extract ◽  
Biological Activities ◽  
Chemical Compounds ◽  
Gas Chromatography Mass Spectrometry ◽  
Pentanoic Acid ◽  
Trogoderma Granarium ◽  
Trans Methyl ◽  
Phenacyl Thiocyanate

Methanolic extract of bioactive compounds of Trogoderma granarium was assayed. GC-MS analysis of Trogoderma granarium revealed the existence of the Pentanoic acid , 1,1-dimethylpropyl ester , (1H)-Pyrimidinone , 5-chloro-4,6- diphenyl, Cyclobutanemethanol , α-methyl- , Nitro-2-methyl-1,3-propanediol , Hydroxylamine ,O-(2-methylpropyl)- , Uridine , 2',3'-O-(phenylmethylene)- ,Acetic acid ,2-benzoylthio-,2-oxo-2-phenylethyl ester , methylpropyl)- , Uridine , 2',3'-O-(phenylmethylene)- , 5'-(4-methylbenzenesulfo , Indolinol , 1-benzoyl-, Benzeneethanol , β-methyl-,(s)- , Acetic acid ,2-benzoylthio-,2-oxo-2-phenylethyl ester , Phenacyl thiocyanate , Deoxy-L-ribose-2,5-dibenzoate , Methenamine , Alanine , N-methyl-n-propargyloxycarbonyl-, decyl ester , Benzoyl chloride , Thiophene-2-ol , benzoate , Ethanone , -(5- nitrotetrazol-2-yl)-1-phenyl- , 2,5-Dimethylhexane-2,5-dihydroperoxide , Benzamide , N-(3-benzylthio-1,2,4-thiadiazol- 5-yl)- , Methyl p-(2-phenyl-1-benzimidazolyl)benzoate , Methyl-2-phenoxyethylamine , Pentaborane(11) , cis-Methoxy- 5-trans-methyl-1R-cyclohexanol , Nitro-1-phenyl-3-(tetrahydropyran-2-yloxy)propan-1-one , cis-Methoxy-5-transmethyl-1R-cyclohexanol. Trogoderma granarium produce many important secondary metabolites with high biological activities.

Study effect of crude extracts of Hibiscus sabdarifa L. on some Enterobacteriaceae

2018 ◽  
Vol 9 (SPL1) ◽  
Author(s):  
Sabreen A Kamal ◽  
Ishraq A Salih ◽  
Hawraa Jawad Kadhim ◽  
Zainab A Tolaifeh
Keyword(s):  
Escherichia Coli ◽  
Ethyl Acetate ◽  
Bacterial Growth ◽  
Chemical Compounds ◽  
Inhibition Zone ◽  
Crude Extracts ◽  
And Control

Red rose or roselle (beauty rose ) is natively known as red tea belong to Malvaceae, it is flowers use traditionally for antihypertensive hepato protective, anticancer,antidiabetic,antibacterial, cytotoxicity and antidiarreal, By preparing red tea from it's flower. In this study, we extract chemical compounds by using two solvent which are Ethanol, Ethyl acetate. so we can extract Anthocyanin which is responsible for red colour of flower with many chemical compounds. then study the effect of these extracts on 5 genera from Enterobacteriacaea which can cause diarrheae (Shigella, Salmonella, Escherichia coli, Proteus and Klebsiella ) by preparing 3 concentrations for each solvent (250, 500, 750 ) mg/ml, and control then compare with two antibiotic (Azereonam 30 mg/ml and Bacitracin 10 mg/ml ) these extracts revealed obvious inhibition zone in bacterial growth.

The Chemistry Decomposition in Human Corpses

2017 ◽  
Vol 68 (6) ◽  
pp. 1352-1356 ◽  
Author(s):  
Beatrice Gabriela Ioan ◽  
Cristiana Manea ◽  
Bianca Hanganu ◽  
Laura Statescu ◽  
Laura Gheuca Solovastru ◽  
...  
Keyword(s):  
Chemical Compounds ◽  
Human Remains ◽  
Organic Substances ◽  
Chemical Decomposition ◽  
Factors Influencing ◽  
Human Decomposition ◽  
Decomposition Processes ◽  
Human Cadavers ◽  
The Subject ◽  
Decomposition Stages

Human body is a complex of organic substances (proteins, lipids, carbohydrates), which undergo chemical decomposition processes soon after death. The compounds released during decomposition characterize the development of different stages of this process: e.g. biogenic amines resulted from the proteins decomposition will confer the particular smell of a cadaver, gases resulted from carbohydrates fermentation will give the bloating aspect of the cadaver. The study of cadaver decomposition and the products resulted from this process is the subject of human taphonomy and is realized nowadays in special facilities in USA and Australia. Identification and analysis of the chemical compounds emerged after human decomposition (gases, liquids, salts) give valuable information to forensic pathologists for estimating the postmortem interval (PMI). More, volatile compounds � which give the odor signature�specific to human remains � may be utilized in identifying clandestine burials, human remains or victims entrapped under ruins in cases of natural disasters. In this paper the authors describe the chemical decomposition stages of human cadavers, the factors influencing these processes and utility for the forensic activity of the results of human taphonomic studies.

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