scholarly journals Matroidal Entropy Functions: A Quartet of Theories of Information, Matroid, Design and Coding

Entropy ◽  
2021 ◽  
Vol 23 (3) ◽  
pp. 323
Author(s):  
Qi Chen ◽  
Minquan Cheng ◽  
Baoming Bai
Keyword(s):  
Coding Theory ◽  
Orthogonal Arrays ◽  
Combinatorial Design ◽  
Combinatorial Structure ◽  
Matroid Theory ◽  
Variable Strength ◽  
Potential Applications ◽  
Connected Matroid ◽  
Entropy Functions ◽  
Extreme Rays

In this paper, we study the entropy functions on extreme rays of the polymatroidal region which contain a matroid, i.e., matroidal entropy functions. We introduce variable strength orthogonal arrays indexed by a connected matroid M and positive integer v which can be regarded as expanding the classic combinatorial structure orthogonal arrays. It is interesting that they are equivalent to the partition-representations of the matroid M with degree v and the (M,v) almost affine codes. Thus, a synergy among four fields, i.e., information theory, matroid theory, combinatorial design, and coding theory is developed, which may lead to potential applications in information problems such as network coding and secret-sharing. Leveraging the construction of variable strength orthogonal arrays, we characterize all matroidal entropy functions of order n≤5 with the exception of log10·U2,5 and logv·U3,5 for some v.

Combinatorial Design of Molecule using Activity-Linked Substructural Topological Information as Applied to Antitubercular Compounds

2018 ◽  
Vol 15 (1) ◽  
pp. 67-81 ◽  
Author(s):  
Chandan Raychaudhury ◽  
Md. Imbesat Hassan Rizvi ◽  
Debnath Pal
Keyword(s):  
Biological Activities ◽  
Combinatorial Design ◽  
Combinatorial Structure ◽  
Potential Drug ◽  
Structure Generation ◽  
Topological Information ◽  
Active Compounds ◽  
Antitubercular Drugs ◽  
Topological Distance ◽  
Drug Molecules

Background: Generating a large number of compounds using combinatorial methods increases the possibility of finding novel bioactive compounds. Although some combinatorial structure generation algorithms are available, any method for generating structures from activity-linked substructural topological information is not yet reported. Objective: To develop a method using graph-theoretical techniques for generating structures of antitubercular compounds combinatorially from activity-linked substructural topological information, predict activity and prioritize and screen potential drug candidates. </P><P> Methods: Activity related vertices are identified from datasets composed of both active and inactive or, differently active compounds and structures are generated combinatorially using the topological distance distribution associated with those vertices. Biological activities are predicted using topological distance based vertex indices and a rule based method. Generated structures are prioritized using a newly defined Molecular Priority Score (MPS). Results: Studies considering a series of Acid Alkyl Ester (AAE) compounds and three known antitubercular drugs show that active compounds can be generated from substructural information of other active compounds for all these classes of compounds. Activity predictions show high level of success rate and a number of highly active AAE compounds produced high MPS score indicating that MPS score may help prioritize and screen potential drug molecules. A possible relation of this work with scaffold hopping and inverse Quantitative Structure-Activity Relationship (iQSAR) problem has also been discussed. The proposed method seems to hold promise for discovering novel therapeutic candidates for combating Tuberculosis and may be useful for discovering novel drug molecules for the treatment of other diseases as well.

scholarly journals On the structure of multipliers ofℤ2

2003 ◽  
Vol 2003 (15) ◽  
pp. 935-946
Author(s):  
Edgar Martínez-Moro ◽  
Roberto Canogar-Mckenzie
Keyword(s):  
Association Scheme ◽  
Coding Theory ◽  
Combinatorial Structure ◽  
Two Dimensional ◽  
Gaussian Integer ◽  
Main Application ◽  
Mannheim Metric ◽  
Signal Constellations

We show the combinatorial structure ofℤ2modulo sublattices similar toℤ2. The tool we use for dealing with this purpose is the notion of association scheme. We classify when the scheme defined by the lattice is imprimitive and characterize its decomposition in terms of the decomposition of the Gaussian integer defining the lattice. This arises in the classification of different forms of tilingℤ2by lattices of this type. The main application of these structures is that they are closely related to two-dimensional signal constellations with a Mannheim metric in the coding theory.

scholarly journals Constructions and Necessities of Some Permutation Polynomials over Finite Fields

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Xiaogang Liu
Keyword(s):  
Finite Field ◽  
Finite Fields ◽  
Coding Theory ◽  
Combinatorial Design ◽  
Permutation Polynomials ◽  
Science And Engineering ◽  
Polynomials Over Finite Fields

Let F q denote the finite field with q elements. Permutation polynomials over finite fields have important applications in many areas of science and engineering such as coding theory, cryptography, and combinatorial design. The study of permutation polynomials has a long history, and many results are obtained in recent years. In this paper, we obtain some further results about the permutation properties of permutation polynomials. Some new classes of permutation polynomials are constructed, and the necessities of some permutation polynomials are studied.

Some Small Circuit-Cocircuit Ramsey Numbers for Matroids

1995 ◽  
Vol 4 (1) ◽  
pp. 67-80 ◽  
Author(s):  
Fair Barbour Hurst ◽  
Talmage James Reid
Keyword(s):  
Positive Integer ◽  
Matroid Theory ◽  
Ramsey Numbers ◽  
Connected Matroid ◽  
Positive Integers

Ramsey numbers for matroids, which mimic properties of Ramsey numbers for graphs, have been denned as follows. Let k and l be positive integers. Then n(k, l) is the least positive integer n such that every connected matroid with n elements contains either a circuit with at least k elements or a cocircuit with at least l elements. We determine the largest known value of these numbers in the sense of maximizing both k and l. We also find extremal matroids with small circuits and cocircuits. Results on matroid connectivity, geometry, and extremal matroid theory are used here.

Calmodulin-mediated gating of lens gap junction channels in vesicles

1984 ◽  
Vol 42 ◽  
pp. 134-137
Author(s):  
Camillo Peracchia ◽  
Stephen J. Girsch
Keyword(s):  
Gap Junctions ◽  
Freeze Fracture ◽  
Orthogonal Arrays ◽  
Eye Lens ◽  
Lens Fiber ◽  
Cell Coupling ◽  
Particle Spacing ◽  
Fiber Cells ◽  
Gap Junction Channels ◽  
Communicating Junctions

The fiber cells of eye lens communicate directly with each other by exchanging ions, dyes and metabolites. In most tissues this type of communication (cell coupling) is mediated by gap junctions. In the lens, the fiber cells are extensively interconnected by junctions. However, lens junctions, although morphologically similar to gap junctions, differ from them in a number of structural, biochemical and immunological features. Like gap junctions, lens junctions are regions of close cell-to-cell apposition. Unlike gap junctions, however, the extracellular gap is apparently absent in lens junctions, such that their thickness is approximately 2 nm smaller than that of typical gap junctions (Fig. 1,c). In freeze-fracture replicas, the particles of control lens junctions are more loosely packed than those of typical gap junctions (Fig. 1,a) and crystallize, when exposed to uncoupling agents such as Ca++, or H+, into pseudo-hexagonal, rhombic (Fig. 1,b) and orthogonal arrays with a particle-to-particle spacing of 6.5 nm. Because of these differences, questions have been raised about the interpretation of the lens junctions as communicating junctions, in spite of the fact that they are the only junctions interlinking lens fiber cells.

An in situ and ex situ TEM study of the formation of thin cobalt silicide films by molecular beam epitaxy on the silicon (100) surface

1988 ◽  
Vol 46 ◽  
pp. 884-885
Author(s):  
D. Loretto ◽  
J. M. Gibson ◽  
S. M. Yalisove ◽  
R. T. Tung
Keyword(s):  
Molecular Beam Epitaxy ◽  
Molecular Beam ◽  
Defect Density ◽  
High Vacuum ◽  
Ultra High Vacuum ◽  
Ex Situ ◽  
Metal Base ◽  
In Situ Experiments ◽  
Potential Applications

The cobalt disilicide/silicon system has potential applications as a metal-base and as a permeable-base transistor. Although thin, low defect density, films of CoSi2 on Si(111) have been successfully grown, there are reasons to believe that Si(100)/CoSi2 may be better suited to the transmission of electrons at the silicon/silicide interface than Si(111)/CoSi2. A TEM study of the formation of CoSi2 on Si(100) is therefore being conducted. We have previously reported TEM observations on Si(111)/CoSi2 grown both in situ, in an ultra high vacuum (UHV) TEM and ex situ, in a conventional Molecular Beam Epitaxy system.The procedures used for the MBE growth have been described elsewhere. In situ experiments were performed in a JEOL 200CX electron microscope, extensively modified to give a vacuum of better than 10-9 T in the specimen region and the capacity to do in situ sample heating and deposition. Cobalt was deposited onto clean Si(100) samples by thermal evaporation from cobalt-coated Ta filaments.

Microstructure of laser-irradiated, conducting Kapton polyimide

1995 ◽  
Vol 53 ◽  
pp. 502-503
Author(s):  
D. L. Callahan ◽  
Z. Ball ◽  
H. M. Phillips ◽  
R. Sauerbrey
Keyword(s):  
Electron Microscopy ◽  
Phase Transition ◽  
Transmission Electron Microscopy ◽  
Cross Section ◽  
Film Surface ◽  
Cross Sectional ◽  
General Utility ◽  
Transmission Electron ◽  
Considerable Debate ◽  
Potential Applications

Ultraviolet laser-irradiation can be used to induce an insulator-to-conductor phase transition on the surface of Kapton polyimide. Such structures have potential applications as resistors or conductors for VLSI applications as well as general utility electrodes. Although the percolative nature of the phase transformation has been well-established, there has been little definitive work on the mechanism or extent of transformation. In particular, there has been considerable debate about whether or not the transition is primarily photothermal in nature, as we propose, or photochemical. In this study, cross-sectional optical microscopy and transmission electron microscopy are utilized to characterize the nature of microstructural changes associated with the laser-induced pyrolysis of polyimide.Laser-modified polyimide samples initially 12 μm thick were prepared in cross-section by standard ultramicrotomy. Resulting contraction in parallel to the film surface has led to distortions in apparent magnification. The scale bars shown are calibrated for the direction normal to the film surface only.

Fabrication and characterization - by High Resolution Electron Microscopy and atom probe microanalysis - of Co-based metallic multilayer films

1990 ◽  
Vol 48 (4) ◽  
pp. 772-773
Author(s):  
Amanda K. Petford-Long ◽  
A. Cerezo ◽  
M.G. Hetherington
Keyword(s):  
Electron Microscopy ◽  
High Resolution ◽  
High Resolution Electron Microscopy ◽  
Atom Probe ◽  
Multilayer Films ◽  
Interface Roughness ◽  
Probe Field ◽  
Resolution Electron ◽  
Potential Applications ◽  
Field Ion Microscope

The fabrication of multilayer films (MLF) with layer thicknesses down to one monolayer has led to the development of materials with unique properties not found in bulk materials. The properties of interest depend critically on the structure and composition of the films, with the interfacial regions between the layers being of particular importance. There are a number of magnetic MLF systems based on Co, several of which have potential applications as perpendicular magnetic (e.g Co/Cr) or magneto-optic (e.g. Co/Pt) recording media. Of particular concern are the effects of parameters such as crystallographic texture and interface roughness, which are determined by the fabrication conditions, on magnetic properties and structure.In this study we have fabricated Co-based MLF by UHV thermal evaporation in the prechamber of an atom probe field-ion microscope (AP). The multilayers were deposited simultaneously onto cobalt field-ion specimens (for AP and position-sensitive atom probe (POSAP) microanalysis without exposure to atmosphere) and onto the flat (001) surface of oxidised silicon wafers (for subsequent study in cross-section using high-resolution electron microscopy (HREM) in a JEOL 4000EX. Deposi-tion was from W filaments loaded with material in the form of wire (Co, Fe, Ni, Pt and Au) or flakes (Cr). The base pressure in the chamber was around 8×10−8 torr during deposition with a typical deposition rate of 0.05 - 0.2nm/s.

Progress and perspectives on halide lithium conductors for all-solid-state lithium batteries

2020 ◽  
Vol 13 (5) ◽  
pp. 1429-1461 ◽  
Author(s):  
Xiaona Li ◽  
Jianwen Liang ◽  
Xiaofei Yang ◽  
Keegan R. Adair ◽  
Changhong Wang ◽  
...  
Keyword(s):  
Energy Storage ◽  
Solid State ◽  
Lithium Batteries ◽  
Electrochemical Stability ◽  
Superionic Conductors ◽  
Fundamental Understanding ◽  
Potential Applications ◽  
Synthesis Routes

This review focuses on fundamental understanding, various synthesis routes, chemical/electrochemical stability of halide-based lithium superionic conductors, and their potential applications in energy storage as well as related challenges.

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