scholarly journals Sharp Bounds on the Spectral Radii of Uniform Hypergraphs concerning Diameter or Clique Number

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Qiannan Niu ◽  
Haizhen Ren ◽  
Lei Zhang
Keyword(s):  
Clique Number ◽  
Fixed Number ◽  
Sharp Bounds ◽  
Uniform Hypergraphs

In this paper, we defined two classes of hypergraphs, hyperbugs and kite hypergraphs. We show that balanced hyperbugs maximize the spectral radii of hypergraphs with fixed number of vertices and diameter and kite hypergraphs minimize the spectral radii of hypergraphs with fixed number of vertices and clique number.

scholarly journals Sharp bounds for ordinary and signless Laplacian spectral radii of uniform hypergraphs

2016 ◽  
Vol 285 ◽  
pp. 217-227 ◽  
Author(s):  
Hongying Lin ◽  
Biao Mo ◽  
Bo Zhou ◽  
Weiming Weng
Keyword(s):  
Sharp Bounds ◽  
Uniform Hypergraphs ◽  
Signless Laplacian

scholarly journals SYMMETRIC AND ASYMMETRIC RAMSEY PROPERTIES IN RANDOM HYPERGRAPHS

2017 ◽  
Vol 5 ◽  
Author(s):  
LUCA GUGELMANN ◽  
RAJKO NENADOV ◽  
YURY PERSON ◽  
NEMANJA ŠKORIĆ ◽  
ANGELIKA STEGER ◽  
...  
Keyword(s):  
Random Graph ◽  
Upper Bound ◽  
Natural Extension ◽  
Fixed Number ◽  
The Other ◽  
Ramsey Problem ◽  
Uniform Hypergraphs ◽  
General Bound ◽  
Random Hypergraphs ◽  
Monochromatic Copy

A celebrated result of Rödl and Ruciński states that for every graph $F$, which is not a forest of stars and paths of length 3, and fixed number of colours $r\geqslant 2$ there exist positive constants $c,C$ such that for $p\leqslant cn^{-1/m_{2}(F)}$ the probability that every colouring of the edges of the random graph $G(n,p)$ contains a monochromatic copy of $F$ is $o(1)$ (the ‘0-statement’), while for $p\geqslant Cn^{-1/m_{2}(F)}$ it is $1-o(1)$ (the ‘1-statement’). Here $m_{2}(F)$ denotes the 2-density of $F$. On the other hand, the case where $F$ is a forest of stars has a coarse threshold which is determined by the appearance of a certain small subgraph in $G(n,p)$. Recently, the natural extension of the 1-statement of this theorem to $k$-uniform hypergraphs was proved by Conlon and Gowers and, independently, by Friedgut, Rödl and Schacht. In particular, they showed an upper bound of order $n^{-1/m_{k}(F)}$ for the 1-statement, where $m_{k}(F)$ denotes the $k$-density of $F$. Similarly as in the graph case, it is known that the threshold for star-like hypergraphs is given by the appearance of small subgraphs. In this paper we show that another type of threshold exists if $k\geqslant 4$: there are $k$-uniform hypergraphs for which the threshold is determined by the asymmetric Ramsey problem in which a different hypergraph has to be avoided in each colour class. Along the way we obtain a general bound on the 1-statement for asymmetric Ramsey properties in random hypergraphs. This extends the work of Kohayakawa and Kreuter, and of Kohayakawa, Schacht and Spöhel who showed a similar result in the graph case. We prove the corresponding 0-statement for hypergraphs satisfying certain balancedness conditions.

scholarly journals Connection between the clique number and the Lagrangian of 3-uniform hypergraphs

2015 ◽  
Vol 10 (4) ◽  
pp. 685-697 ◽  
Author(s):  
Qingsong Tang ◽  
Yuejian Peng ◽  
Xiangde Zhang ◽  
Cheng Zhao
Keyword(s):  
Clique Number ◽  
Uniform Hypergraphs

scholarly journals Extremal Problems for Independent Set Enumeration

10.37236/656 ◽  
2011 ◽  
Vol 18 (1) ◽  
Author(s):  
Jonathan Cutler ◽  
A. J. Radcliffe
Keyword(s):  
Initial Segment ◽  
Independence Number ◽  
Independent Set ◽  
Independent Sets ◽  
Clique Number ◽  
Extremal Problems ◽  
Fixed Number ◽  
Regular Graphs ◽  
Minimum Number ◽  
Rich History

The study of the number of independent sets in a graph has a rich history. Recently, Kahn proved that disjoint unions of $K_{r,r}$'s have the maximum number of independent sets amongst $r$-regular bipartite graphs. Zhao extended this to all $r$-regular graphs. If we instead restrict the class of graphs to those on a fixed number of vertices and edges, then the Kruskal-Katona theorem implies that the graph with the maximum number of independent sets is the lex graph, where edges form an initial segment of the lexicographic ordering. In this paper, we study three related questions. Firstly, we prove that the lex graph has the maximum number of weighted independent sets for any appropriate weighting. Secondly, we solve the problem of maximizing the number of independents sets in graphs with specified independence number or clique number. Finally, for $m\leq n$, we find the graphs with the minimum number of independent sets for graphs with $n$ vertices and $m$ edges.

Interactive multiobjective DEA target setting using lexicographic DDF

2020 ◽  
Vol 54 (6) ◽  
pp. 1703-1722 ◽  
Author(s):  
Narges Soltani ◽  
Sebastián Lozano
Keyword(s):  
Efficient Frontier ◽  
Directional Distance Function ◽  
Fixed Number ◽  
Optimization Approach ◽  
Target Setting ◽  
Interactive Process ◽  
Decision Making Unit ◽  
Setting Approach ◽  
Promising Area ◽  
Current Region

In this paper, a new interactive multiobjective target setting approach based on lexicographic directional distance function (DDF) method is proposed. Lexicographic DDF computes efficient targets along a specified directional vector. The interactive multiobjective optimization approach consists in several iteration cycles in each of which the Decision Making Unit (DMU) is presented a fixed number of efficient targets computed corresponding to different directional vectors. If the DMU finds one of them promising, the directional vectors tried in the next iteration are generated close to the promising one, thus focusing the exploration of the efficient frontier on the promising area. In any iteration the DMU may choose to finish the exploration of the current region and restart the process to probe a new region. The interactive process ends when the DMU finds its most preferred solution (MPS).

Phospholipid-Protein Interactions in the Formation of Prothrombin Activator

1965 ◽  
Vol 14 (03/04) ◽  
pp. 431-444 ◽  
Author(s):  
E. R Cole ◽  
J. L Koppel ◽  
J. H Olwin
Keyword(s):  
Complex Formation ◽  
Protein Interactions ◽  
Calcium Ions ◽  
Fixed Number ◽  
Factor V ◽  
Clotting Factors ◽  
Number Of Binding Sites ◽  
C Complex ◽  
Autoprothrombin C

SummarySince Ac-globulin (factor V) is involved in the formation of prothrombin activator, its ability to complex with phospholipids was studied. Purified bovine Ac-globulin was complexed to asolectin, there being presumably a fixed number of binding sites on the phospholipid micelle for Ac-globulin. In contrast to the requirement for calcium ions in the formation of complexes between asolectin and autoprothrombin C, calcium ions were not required for complex formation between asolectin and Ac-globulin to occur ; in fact, the presence of calcium prevented complex formation occurring, the degree of inhibition being dependent on the calcium concentration. By treating isolated, pre-formed aso- lectin-Ac-globulin complexes with calcium chloride solutions, Ac-globulin could be recovered in a much higher state of purity and essentially free of asolectin.Complete activators were formed by first preparing the asolectin-calcium- autoprothrombin C complex and then reacting the complex with Ac-globulin. A small amount of this product was very effective as an activator of purified prothrombin without further addition of calcium or any other cofactor. If the autoprothrombin C preparation used to prepare the complex was free of traces of prothrombin, the complete activator was stable for several hours at room temperature. Stable preparations of the complete activator were centrifuged, resulting in the sedimentation of most of the activity. Experimental evidence also indicated that activator activity was highest when autoprothrombin C and Ac-globulin were complexed to the same phospholipid micelle, rather than when the two clotting factors were complexed to separate micelles. These data suggested that the in vivo prothrombin activator may be a sedimentable complex composed of a thromboplastic enzyme, calcium, Ac-globulin and phospholipid.

A Correspondence-Free Color Chart Design for Color Calibration

2020 ◽  
Vol 2020 (1) ◽  
pp. 100-104
Author(s):  
Hakki Can Karaimer ◽  
Rang Nguyen
Keyword(s):  
Color Space ◽  
Fixed Number ◽  
New Approach ◽  
Color Chart ◽  
Color Calibration ◽  
Space Transformation ◽  
Color Space Transformation ◽  
Chart Design ◽  
Calibration Approach

Colorimetric calibration computes the necessary color space transformation to map a camera's device-specific color space to a device-independent perceptual color space. Color calibration is most commonly performed by imaging a color rendition chart with a fixed number of color patches with known colorimetric values (e. g., CIE XYZ values). The color space transformation is estimated based on the correspondences between the camera's image and the chart's colors. We present a new approach to colorimetric calibration that does not require explicit color correspondences. Our approach computes a color space transformation by aligning the color distributions of the captured image to the known distribution of a calibration chart containing thousands of colors. We show that a histogram-based colorimetric calibration approach provides results that are onpar with the traditional patch-based method without the need to establish correspondences.

A Brief Survey on Text Classification Using Various Machine Learning Techniques

2018 ◽  
Vol 8 (1) ◽  
pp. 14
Author(s):  
Padmavathi .S ◽  
M. Chidambaram
Keyword(s):  
Machine Learning ◽  
Text Classification ◽  
Fixed Number ◽  
Machine Learning Techniques ◽  
Online Information ◽  
Rule Based ◽  
Learning Techniques ◽  
Machine Learning Approach ◽  
Rule Based Approach

Text classification has grown into more significant in managing and organizing the text data due to tremendous growth of online information. It does classification of documents in to fixed number of predefined categories. Rule based approach and Machine learning approach are the two ways of text classification. In rule based approach, classification of documents is done based on manually defined rules. In Machine learning based approach, classification rules or classifier are defined automatically using example documents. It has higher recall and quick process. This paper shows an investigation on text classification utilizing different machine learning techniques.

Sign in / Sign up

Export Citation Format

Share Document