The Minimum Size of Saturated Hypergraphs

1999 ◽  
Vol 8 (5) ◽  
pp. 483-492 ◽  
Author(s):  
OLEG PIKHURKO
Keyword(s):  
Finite Family ◽  
Minimum Size ◽  
Set Systems ◽  
Minimum Number

Let [Fscr ] be a family of forbidden k-hypergraphs (k-uniform set systems). An [Fscr ]-saturated hypergraph is a maximal k-uniform set system not containing any member of [Fscr ]. As the main result we prove that, for any finite family [Fscr ], the minimum number of edges of an [Fscr ]-saturated hypergraph is O(nk−1). In particular, this implies a conjecture of Tuza. Some other related results are presented.

IDENTIFYING CO-REGULATING MICRORNA GROUPS

2010 ◽  
Vol 08 (01) ◽  
pp. 99-115 ◽  
Author(s):  
JIYUAN AN ◽  
KWOK PUI CHOI ◽  
CHRISTINE A. WELLS ◽  
YI-PING PHOEBE CHEN
Keyword(s):  
Neurodegenerative Diseases ◽  
Target Genes ◽  
Signal To Noise Ratio ◽  
Statistical Tests ◽  
False Positive Rate ◽  
Target Prediction ◽  
Minimum Size ◽  
Supplementary Information ◽  
P Value ◽  
Minimum Number

Background: Current miRNA target prediction tools have the common problem that their false positive rate is high. This renders identification of co-regulating groups of miRNAs and target genes unreliable. In this study, we describe a procedure to identify highly probable co-regulating miRNAs and the corresponding co-regulated gene groups. Our procedure involves a sequence of statistical tests: (1) identify genes that are highly probable miRNA targets; (2) determine for each such gene, the minimum number of miRNAs that co-regulate it with high probability; (3) find, for each such gene, the combination of the determined minimum size of miRNAs that co-regulate it with the lowest p-value; and (4) discover for each such combination of miRNAs, the group of genes that are co-regulated by these miRNAs with the lowest p-value computed based on GO term annotations of the genes. Results: Our method identifies 4, 3 and 2-term miRNA groups that co-regulate gene groups of size at least 3 in human. Our result suggests some interesting hypothesis on the functional role of several miRNAs through a "guilt by association" reasoning. For example, miR-130, miR-19 and miR-101 are known neurodegenerative diseases associated miRNAs. Our 3-term miRNA table shows that miR-130/19/101 form a co-regulating group of rank 22 (p-value =1.16 × 10-2). Since miR-144 is co-regulating with miR-130, miR-19 and miR-101 of rank 4 (p-value = 1.16 × 10-2) in our 4-term miRNA table, this suggests hsa-miR-144 may be neurodegenerative diseases related miRNA. Conclusions: This work identifies highly probable co-regulating miRNAs, which are refined from the prediction by computational tools using (1) signal-to-noise ratio to get high accurate regulating miRNAs for every gene, and (2) Gene Ontology to obtain functional related co-regulating miRNA groups. Our result has partly been supported by biological experiments. Based on prediction by TargetScanS, we found highly probable target gene groups in the Supplementary Information. This result might help biologists to find small set of miRNAs for genes of interest rather than huge amount of miRNA set. Supplementary Information:.

scholarly journals Optimal Testing and Design of Adders

VLSI Design ◽  
1994 ◽  
Vol 1 (4) ◽  
pp. 285-298 ◽  
Author(s):  
Michael J. Batek ◽  
John P. Hayes
Keyword(s):  
Performance Optimization ◽  
Minimum Size ◽  
Optimal Test ◽  
Test Set ◽  
Tree Structures ◽  
Ripple Carry Adder ◽  
Conflicting Objectives ◽  
Minimum Number ◽  
Test Sets ◽  
And Performance

On-the-fly calculations of area and performance are a typical part of the computer-aided iterative design process in VLSI, which aims at a satisfactory tradeoff of various conflicting objectives, among which are test-generation time and test-set size. However, determining test sets on-the-fly as one circuit is transformed into another is extremely difficult. Our goal is to add a test dimension to the design optimization process that complements methods concerned with area and performance optimization. We define a set of logic transformations that result in easily computed changes to test sets. Test-set preserving (TSP) transformations preserve a combinational circuit’s test sets, while test-set altering (TSA) transformations introduce a minimum number of tests needed to maintain completeness. We illustrate our approach with a family of adders that share area-efficient tree structures and differ in the amount of carry-lookahead used to accelerate carry computation. Members include the ripple-carry adder, which has no lookahead, and the standard carry-lookahead adder, which exploits lookahead across all inputs. It is straightforward to derive area and performance measures for this class of adders. Given an n-bit adder with lookahead degree k, we determine a sequence of circuit transformations that produce the adder of degree k2 and test sets of minimum size. Optimal test sets of size k(logkn + 1) + 2 result for arbitrary n and k, which improve significantly upon previously reported tests.

scholarly journals Covering Partial Cubes with Zones

10.37236/5076 ◽  
2015 ◽  
Vol 22 (3) ◽  
Author(s):  
Jean Cardinal ◽  
Stefan Felsner
Keyword(s):  
Isometric Embedding ◽  
Linear Extension ◽  
Upper And Lower Bounds ◽  
Minimum Size ◽  
Worst Case ◽  
Line Arrangement ◽  
Minimal Dimension ◽  
Special Cases ◽  
Minimum Number ◽  
Partial Cube

A partial cube is a graph having an isometric embedding in a hypercube. Partial cubes are characterized by a natural equivalence relation on the edges, whose classes are called zones. The number of zones determines the minimal dimension of a hypercube in which the graph can be embedded. We consider the problem of covering the vertices of a partial cube with the minimum number of zones. The problem admits several special cases, among which are the following:cover the cells of a line arrangement with a minimum number of lines,select a smallest subset of edges in a graph such that for every acyclic orientation, there exists a selected edge that can be flipped without creating a cycle,find a smallest set of incomparable pairs of elements in a poset such that in every linear extension, at least one such pair is consecutive,find a minimum-size fibre in a bipartite poset.We give upper and lower bounds on the worst-case minimum size of a covering by zones in several of those cases. We also consider the computational complexity of those problems, and establish some hardness results.

scholarly journals Fractional Strong Matching Preclusion of Split-Star Networks

2019 ◽  
Vol 11 (4) ◽  
pp. 32
Author(s):  
Ping Han ◽  
Yuzhi Xiao ◽  
Chengfu Ye ◽  
He Li
Keyword(s):  
Perfect Matching ◽  
Minimum Size ◽  
Star Networks ◽  
Minimum Number

The matching preclusion number of graph G is the minimum size of edges whose deletion leaves the resulting graph without a perfect matching or an almost perfect matching. Let F be an edge subset and F′ be a subset of edges and vertices of a graph G. If G − F and G − F′ have no fractional matching preclusion, then F is a fractional matching preclusion (FMP) set, and F ′is a fractional strong matching preclusion (FSMP) set of G. The FMP (FSMP) number of G is the minimum number of FMP (FSMP) set of G. In this paper, we study fractional matching preclusion number and fractional strong matching preclusion number of split-star networks. Moreover, We categorize all the optimal fractional strong matching preclusion sets of split-star networks.

scholarly journals Hypergraph Saturation Irregularities

10.37236/7727 ◽  
2018 ◽  
Vol 25 (2) ◽  
Author(s):  
Natalie C. Behague
Keyword(s):  
Finite Family ◽  
Minimum Number ◽  
Saturation Number

Let $\mathcal{F}$ be a family of $r$-graphs. An $r$-graph $G$ is called $\mathcal{F}$-saturated if it does not contain any members of $\mathcal{F}$ but adding any edge creates a copy of some $r$-graph in $\mathcal{F}$. The saturation number $\operatorname{sat}(\mathcal{F},n)$ is the minimum number of edges in an $\mathcal{F}$-saturated graph on $n$ vertices. We prove that there exists a finite family $\mathcal{F}$ such that $\operatorname{sat}(\mathcal{F},n) / n^{r-1}$  does not tend to a limit. This settles a question of Pikhurko.

scholarly journals Minimum survivable graphs with bounded distance increase

2003 ◽  
Vol Vol. 6 no. 1 ◽  
Author(s):  
Selma Djelloul ◽  
Mekkia Kouider
Keyword(s):  
Fault Tolerance ◽  
Lower Bounds ◽  
Interconnection Networks ◽  
Negative Integer ◽  
Upper And Lower Bounds ◽  
Minimum Size ◽  
Np Hard ◽  
Bounded Distance ◽  
Minimum Number ◽  
International Audience

International audience We study in graphs properties related to fault-tolerance in case a node fails. A graph G is k-self-repairing, where k is a non-negative integer, if after the removal of any vertex no distance in the surviving graph increases by more than k. In the design of interconnection networks such graphs guarantee good fault-tolerance properties. We give upper and lower bounds on the minimum number of edges of a k-self-repairing graph for prescribed k and n, where n is the order of the graph. We prove that the problem of finding, in a k-self-repairing graph, a spanning k-self-repairing subgraph of minimum size is NP-Hard.

scholarly journals Constructive Upper Bounds for Cycle-Saturated Graphs of Minimum Size

10.37236/1055 ◽  
2006 ◽  
Vol 13 (1) ◽  
Author(s):  
Ronald Gould ◽  
Tomasz Łuczak ◽  
John Schmitt
Keyword(s):  
Upper Bounds ◽  
Minimum Size ◽  
Saturated Graphs ◽  
Minimum Number

A graph $G$ is said to be $C_l$-saturated if $G$ contains no cycle of length $l$, but for any edge in the complement of $G$ the graph $G+e$ does contain a cycle of length $l$. The minimum number of edges of a $C_l$-saturated graph was shown by Barefoot et al. to be between $n+c_1{n\over l}$ and $n+c_2{n\over l}$ for some positive constants $c_1$ and $c_2$. This confirmed a conjecture of Bollobás. Here we improve the value of $c_2$ for $l \geq 8$.

scholarly journals THE PROBLEM OF EMPLACEMENT OF TRIANGULAR GEOMETRIC NET ON THE SPHERE WITH NODES ON THE SAME LEVEL

2017 ◽  
Vol 13 (2) ◽  
pp. 154-160 ◽  
Author(s):  
Vasilij D. Antoshkin
Keyword(s):  
Spherical Triangle ◽  
Minimum Size ◽  
Effective Solution ◽  
Shortest Distance ◽  
Minimum Number ◽  
Triangular Network ◽  
Spherical Triangles

One of the methods of formation of triangular networks in the field is investigated. Conditions of the problem of locating a triangular network in the area are delivered. The criterion for assessing the effectiveness of the solution of the problem is the minimum number of sizes of the dome panels, the possibility of pre-assembly and pre-stressing. The solution of the problem of one embodiment of a triangular network of accommodation in a compatible spherical triangle and, accordingly, on the sphere. Placing on the area of regular and irregular hexagon inscribed in a circle, ie, flat figures or composed in turn of spherical triangles with minimum dimensions of the ribs, is an effective solution in the form of a network formed by circles of minimum radii, ie, circles on a sphere obtained at the touch of three adjacent circles whose centers are at the shortest distance from each other. Task align the supports at one level can be resolved by placement in the regular hexagons and irregular pentagons hexagonsinscribed in a circle of minimum size.

scholarly journals The minimum number of disjoint pairs in set systems and related problems

COMBINATORICA ◽  
2016 ◽  
Vol 36 (6) ◽  
pp. 623-660 ◽  
Author(s):  
Shagnik Das ◽  
Wenying Gan ◽  
Benny Sudakov
Keyword(s):  
Set Systems ◽  
Minimum Number

scholarly journals Fungicidal effect of some non-conventional chemicals for management of alternaria blight disease of mustard

2014 ◽  
Vol 6 (2) ◽  
pp. 913-919
Author(s):  
Amarendra Kumar ◽  
Santosh Kumar ◽  
Rakesh Kumar ◽  
Gireesh Chand ◽  
S. J. Kolte
Keyword(s):  
Foliar Spray ◽  
Calcium Sulphate ◽  
Limiting Factors ◽  
Minimum Size ◽  
Yield Losses ◽  
Alternaria Blight ◽  
Fungicidal Effect ◽  
Leaf Spots ◽  
Minimum Number ◽  
Blight Disease

Alternaria blight disease of mustard caused by a necrotrophic fungus Alternaria brassicae (Berk.) Sacc. Is one of the most important limiting factors, causing yield losses of up to 47% in mustard (Brassica juncea). The aim of this present investigation was to evaluate the fungicidal effect of non-conventional chemicals viz. calcium sulphate (CaSO4), potassium chloride (KCl), potassium sulphate (K2SO4), zinc sulphate (ZnSO4) and borax (Na2B4O7.10H2O) against alternaria blight disease of mustard. The significantly minimum size of spot was recorded in T1 CaS at 0.5% (1.73) followed by T3 CaS at 1.5% (1.75) and T2 CaS at 1.0% (1.78) respectively in comparison to check. The minimum number of average leaf spots/25 mm2 leaf area was observed in T3 CaS at 1.5% (1.78) followed by T1 CaS at 0.5% (2.26). T1 CaS @ at 0.5% showed significantly lowest disease index (13.00%) followed by T15 NaB at 0.75% (17.77%) and T8 KS at 1.0% (18.00%) respectively over check. The average minimum apparent infection rate was recorded in T1 CaS at 0.5% ( 0.504) followed by T9 KS at 1.5% (0.553) and T3 CaS at 1.5% (0.573) respectively. The AUDPC was significantly minimum in all the treatments of CaSO4 i.e. in T1 CaS at 0.5% (32.25), T2 CaS at 1.0% (33.8) and T3 CaS at 1.5% (35.55) in comparison to check (77.95). The foliar spray of CaSO4 at 0.5% concentration induced resistance significantly against alternaria blight and reduce pesticide residue in food and environment.

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