Panchromatic colorings of random hypergraphs

2021 ◽  
Vol 31 (1) ◽  
pp. 19-41
Author(s):  
D. A. Kravtsov ◽  
N. E. Krokhmal ◽  
D. A. Shabanov
Keyword(s):  
Binomial Model ◽  
Threshold Probability ◽  
The Difference ◽  
Random Hypergraphs

Abstract We study the threshold probability for the existence of a panchromatic coloring with r colors for a random k-homogeneous hypergraph in the binomial model H(n, k, p), that is, a coloring such that each edge of the hypergraph contains the vertices of all r colors. It is shown that this threshold probability for fixed r < k and increasing n corresponds to the sparse case, i. e. the case p = c n / ( n k ) $p = cn/{n \choose k}$ for positive fixed c. Estimates of the form c 1(r, k) < c < c 2(r, k) for the parameter c are found such that the difference c 2(r, k) − c 1(r, k) converges exponentially fast to zero if r is fixed and k tends to infinity.

scholarly journals Jigsaw percolation on random hypergraphs

2017 ◽  
Vol 54 (4) ◽  
pp. 1261-1277 ◽  
Author(s):  
Béla Bollobás ◽  
Oliver Cooley ◽  
Mihyun Kang ◽  
Christoph Koch
Keyword(s):  
Social Networks ◽  
Common Vertex ◽  
Critical Threshold ◽  
Threshold Probability ◽  
Percolation Process ◽  
Asymptotic Order ◽  
Vertex Set ◽  
Random Hypergraphs

AbstractThe jigsaw percolation process on graphs was introduced by Brummittet al.(2015) as a model of collaborative solutions of puzzles in social networks. Percolation in this process may be viewed as the joint connectedness of two graphs on a common vertex set. Our aim is to extend a result of Bollobáset al.(2017) concerning this process to hypergraphs for a variety of possible definitions of connectedness. In particular, we determine the asymptotic order of the critical threshold probability for percolation when both hypergraphs are chosen binomially at random.

scholarly journals Hamiltonian Berge cycles in random hypergraphs

2020 ◽  
pp. 1-11
Author(s):  
Deepak Bal ◽  
Ross Berkowitz ◽  
Pat Devlin ◽  
Mathias Schacht
Keyword(s):  
Optimal Stopping ◽  
High Probability ◽  
Minimum Degree ◽  
Stopping Time ◽  
Threshold Probability ◽  
Optimal Stopping Time ◽  
Uniform Hypergraphs ◽  
Time Result ◽  
Random Hypergraphs

Abstract In this note we study the emergence of Hamiltonian Berge cycles in random r-uniform hypergraphs. For $r\geq 3$ we prove an optimal stopping time result that if edges are sequentially added to an initially empty r-graph, then as soon as the minimum degree is at least 2, the hypergraph with high probability has such a cycle. In particular, this determines the threshold probability for Berge Hamiltonicity of the Erdős–Rényi random r-graph, and we also show that the 2-out random r-graph with high probability has such a cycle. We obtain similar results for weak Berge cycles as well, thus resolving a conjecture of Poole.

scholarly journals A Normalized Congruent Matching Area Method for the Correlation of Breech Face Impression Images

2018 ◽  
Vol 123 ◽  
Author(s):  
Zhe Chen ◽  
John Song ◽  
Wei Chu ◽  
Mingsi Tong ◽  
XueZeng Zhao
Keyword(s):  
Probability Distribution ◽  
Three Dimensional ◽  
Binomial Model ◽  
Optimal Range ◽  
Cell Pair ◽  
Identification Criterion ◽  
Optical Images ◽  
The Difference ◽  
Image Pairs ◽  
Cartridge Cases

The congruent matching cells (CMC) method was invented at the National Institute of Standards and Technology (NIST) for firearm evidence identification and error rate estimation. The CMC method divides the correlated image pairs into cells and uses four parameters to quantify topography similarity and pattern congruency of the correlated cell pairs in firearm breech face impressions on fired cartridge cases. A preliminary conservative numerical identification criterion of C = 6 CMCs was suggested for identifying images of cartridge cases fired from the same firearm. The CMC method was validated by correlations using both three-dimensional (3D) topography images and two-dimensional (2D) optical images from a set of 40 cartridge cases fired from a firearm set composed of 10 consecutively manufactured pistol slides. However, in the original CMC method, due to the difference in the effective data area of the correlated cells, final CMCs obtained from an image pair presented different data quantity (or validity level), and thus the empirical criterion C = 6 CMCs did not remain optimal for identification when the correlated cell size changed. In this study, a normalized congruent matching area (NCMA) method that considers the difference in the data area in each correlated cell pair was developed. Based on the NCMA method, an optimal range of cell sizes for breech face identification with granular characteristics was determined. A binomial model was used to fit the known nonmatching NCMA probability distribution ΨNCMA, and a beta-binomial model was used to fit the known matching NCMA probability distribution ΦNCMA. An experimental improvement in the normalized identification criterion C of around 6 % was observed in the validation tests when the cell sizes were in the optimal range.

scholarly journals O wykorzystaniu modelu dwumianowego do optymalizacji strategii sprzedaży zboża

2018 ◽  
pp. 69-79
Author(s):  
Marek Kociński
Keyword(s):  
Optimal Choice ◽  
Numerical Calculations ◽  
Binomial Model ◽  
The Difference ◽  
The Moment ◽  
The Cost ◽  
Theoretical Results ◽  
Better Than

In the article the problem of the optimal choice of the moment of selling the grain is considered when the grain price is characterized by volatility and there is the costs of storing the grain. To solve the problem of maximizing the difference between the amount obtained for the grain sale and the cost of storing the grain a binomial model was used to describe the dynamics of the grain price. The theoretical results of the paper were applied to the numerical calculations. In the optimization of selling the grain, the strategy with the random selling moment may be significantly better than the strategy with the deterministic selling time.

scholarly journals Development of Urinary Diagnostic Biomarker for IgA Nephropathy by Lectin Microarray

2021 ◽  
pp. 1-11
Author(s):  
Yasuhiro Onishi ◽  
Koki Mise ◽  
Chieko Kawakita ◽  
Haruhito A. Uchida ◽  
Hitoshi Sugiyama ◽  
...  
Keyword(s):  
Model Fitting ◽  
T Antigen ◽  
University Hospital ◽  
Reference Standard ◽  
Net Benefit ◽  
Threshold Probability ◽  
Discriminatory Ability ◽  
Lectin Microarray ◽  
Serum Iga ◽  
The Difference

<b><i>Introduction:</i></b> The pathogenic roles of aberrantly glycosylated IgA1 have been reported. However, it is unexplored whether the profiling of urinary glycans contributes to the diagnosis of IgAN. <b><i>Methods:</i></b> We conducted a retrospective study enrolling 493 patients who underwent renal biopsy at Okayama University Hospital between December 2010 and September 2017. We performed lectin microarray in urine samples and investigated whether c-statistics of the reference standard diagnosis model employing hematuria, proteinuria, and serum IgA were improved by adding the urinary glycan intensity. <b><i>Results:</i></b> Among 45 lectins, 3 lectins showed a significant improvement of the models: <i>Amaranthus caudatus</i> lectin (ACA) with the difference of c-statistics 0.038 (95% CI: 0.019–0.058, <i>p</i> &#x3c; 0.001), <i>Agaricus bisporus</i> lectin (ABA) 0.035 (95% CI: 0.015–0.055, <i>p</i> &#x3c; 0.001), and <i>Maackia amurensis</i> lectin (MAH) 0.035 (95% CI: 0.015–0.054, <i>p</i> &#x3c; 0.001). In 3 lectins, each signal plus reference standard showed good reclassification (category-free NRI and relative IDI) and good model fitting associated with the improvement of AIC and BIC. Stratified by eGFR, the discriminatory ability of ACA plus reference standard was maintained, suggesting the robust renal function-independent diagnostic performance of ACA. By decision curve analysis, there was a 3.45% net benefit by adding urinary glycan intensity of ACA to the reference standard at the predefined threshold probability of 40%. <b><i>Conclusions:</i></b> The reduction of Gal(β1-3)GalNAc (T-antigen), Sia(α2-3)Gal(β1-3)GalNAc (Sialyl T), and Sia(α2-3)Gal(β1-3)Sia(α2-6)GalNAc (disialyl-T) was suggested by binding specificities of 3 lectins. C1GALT1 and COSMC were responsible for the biosynthesis of these glycans, and they were known to be downregulated in IgAN. The urinary glycan analysis by ACA is a useful and robust noninvasive strategy for the diagnosis of IgAN.

scholarly journals A REVIEW OF THE METHODS OF ECONOMIC AND MATHEMATICAL MODELING BASED ON THE PRINCIPLES OF ECONOPHYSICS. PART 1

2020 ◽  
pp. 161-181
Author(s):  
Dmitrii Andrianov ◽  
◽  
Petr Simonov ◽  
Keyword(s):  
Information Systems ◽  
Empirical Distribution ◽  
Supply And Demand ◽  
Time Interval ◽  
Mathematical Methods ◽  
Threshold Probability ◽  
Infinite Cluster ◽  
Arbitrage Opportunities ◽  
Financial Bubble ◽  
The Difference

A review of theoretical and applied results obtained in the framework of the scientific direction in econophysics at the Department of Information Systems and Mathematical Methods in Economics is given. The first part gives the concept of a financial bubble and methods for their search. The review covers the period 2010-2019. A review of theoretical and applied results obtained in the framework of the scientific direction in econophysics at the Department of information systems and mathematical methods in Economics is given. The first part gives the concept of a financial bubble and methods for finding them. At the beginning of the article, the development of econophysics is given. Therefore, using the research of physicists as a model, econophysics should begin its research not from the upper floors of an economic building (in the form of financial markets, distribution of returns on financial assets, etc.), but from its fundamental foundations or, in the words of physicists, from elementary economic objects and forms of their movement (labor, its productivity, etc.). Only in this way can econophysics find its subject of study and become a "new form of economic theory". Further, the main prerequisites of financial bubble models in the market are considered: the principle of the absence of arbitrage opportunities, the existence of rational agents, a risk-driven model, and a price-driven model. A well-known nonlinear LPPL model (log periodic power law model) was proposed. In the works of V. O. Arbuzov, it was proposed to use procedures for selecting models. Namely, basic selection, "stationarity" filtering, and spectral analysis were introduced. The results of the model were presented in the works of D. Sornette and his students. The second part gives the concept of percolation and its application in Economics. We will consider a mathematical model proposed by J. P. Bouchaud, D. Stauffer, and D. Sornette that recreates the behavior of an agent in the market and their interaction, geometrically describing a phase transition of the second kind. In this model, the price of an asset in a single time interval changes in proportion to the difference between supply and demand in this market. The key situation to study is the moment of formation of an infinite cluster on the percolation grid, since this means the collapse of the market, when the overwhelming part of agents for this market has a similar opinion about their actions to buy or sell an asset. The main characteristics of the process are the threshold probability of market collapse, as well as the empirical distribution function of price changes in this market.

The Origin of the Moon

1962 ◽  
Vol 14 ◽  
pp. 149-155 ◽  
Author(s):  
E. L. Ruskol
Keyword(s):  
Chemical Composition ◽  
Solar System ◽  
The Moon ◽  
The Earth ◽  
The Difference ◽  
Origin Of The Moon

The difference between average densities of the Moon and Earth was interpreted in the preceding report by Professor H. Urey as indicating a difference in their chemical composition. Therefore, Urey assumes the Moon's formation to have taken place far away from the Earth, under conditions differing substantially from the conditions of Earth's formation. In such a case, the Earth should have captured the Moon. As is admitted by Professor Urey himself, such a capture is a very improbable event. In addition, an assumption that the “lunar” dimensions were representative of protoplanetary bodies in the entire solar system encounters great difficulties.

Influence of Cell Wall Composition on the Fossilisation of Bacteria and the Implications for the Search for Early Life Forms

1997 ◽  
Vol 161 ◽  
pp. 491-504 ◽  
Author(s):  
Frances Westall
Keyword(s):  
Cell Wall ◽  
Life Forms ◽  
Cation Binding ◽  
Positive Bacterium ◽  
Gram Positive ◽  
Gram Positive Bacteria ◽  
Transmission Electron ◽  
Hydrothermal Sediments ◽  
Identification Of Bacteria ◽  
The Difference

AbstractThe oldest cell-like structures on Earth are preserved in silicified lagoonal, shallow sea or hydrothermal sediments, such as some Archean formations in Western Australia and South Africa. Previous studies concentrated on the search for organic fossils in Archean rocks. Observations of silicified bacteria (as silica minerals) are scarce for both the Precambrian and the Phanerozoic, but reports of mineral bacteria finds, in general, are increasing. The problems associated with the identification of authentic fossil bacteria and, if possible, closer identification of bacteria type can, in part, be overcome by experimental fossilisation studies. These have shown that not all bacteria fossilise in the same way and, indeed, some seem to be very resistent to fossilisation. This paper deals with a transmission electron microscope investigation of the silicification of four species of bacteria commonly found in the environment. The Gram positiveBacillus laterosporusand its spore produced a robust, durable crust upon silicification, whereas the Gram negativePseudomonas fluorescens, Ps. vesicularis, andPs. acidovoranspresented delicately preserved walls. The greater amount of peptidoglycan, containing abundant metal cation binding sites, in the cell wall of the Gram positive bacterium, probably accounts for the difference in the mode of fossilisation. The Gram positive bacteria are, therefore, probably most likely to be preserved in the terrestrial and extraterrestrial rock record.

Structuring, Motions and Shapes of Corona Emission Line Profiles

1994 ◽  
Vol 144 ◽  
pp. 421-426
Author(s):  
N. F. Tyagun
Keyword(s):  
Emission Line ◽  
Filling Factor ◽  
Direct Relationship ◽  
Coronal Plasma ◽  
Line Of Sight ◽  
Line Profiles ◽  
The Difference ◽  
Yellow Line ◽  
Red Line

AbstractThe interrelationship of half-widths and intensities for the red, green and yellow lines is considered. This is a direct relationship for the green and yellow line and an inverse one for the red line. The difference in the relationships of half-widths and intensities for different lines appears to be due to substantially dissimilar structuring and to a set of line-of-sight motions in ”hot“ and ”cold“ corona regions.When diagnosing the coronal plasma, one cannot neglect the filling factor - each line has such a factor of its own.

Difference Fourier Analysis of Glucose Embedded and Frozen Hydrated Purple Membrane

1982 ◽  
Vol 40 ◽  
pp. 74-75
Author(s):  
Jules S. Jaffe ◽  
Robert M. Glaeser
Keyword(s):  
Purple Membrane ◽  
Data Set ◽  
High Resolution Data ◽  
X Ray ◽  
X Ray Crystallography ◽  
Fourier Techniques ◽  
Versus Protein ◽  
The Difference ◽  
Difference Fourier ◽  
Ideal Method

Although difference Fourier techniques are standard in X-ray crystallography it has only been very recently that electron crystallographers have been able to take advantage of this method. We have combined a high resolution data set for frozen glucose embedded Purple Membrane (PM) with a data set collected from PM prepared in the frozen hydrated state in order to visualize any differences in structure due to the different methods of preparation. The increased contrast between protein-ice versus protein-glucose may prove to be an advantage of the frozen hydrated technique for visualizing those parts of bacteriorhodopsin that are embedded in glucose. In addition, surface groups of the protein may be disordered in glucose and ordered in the frozen state. The sensitivity of the difference Fourier technique to small changes in structure provides an ideal method for testing this hypothesis.

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