scholarly journals Extremal Hypergraphs for the Biased Erdős-Selfridge Theorem

10.37236/2394 ◽  
2013 ◽  
Vol 20 (1) ◽  
Author(s):  
Eric Lars Sundberg
Keyword(s):  
Winning Strategy ◽  
Simple Criterion ◽  
Uniform Hypergraphs ◽  
Positional Games ◽  
Extremal Hypergraph

A positional game is essentially a generalization of Tic-Tac-Toe played on a hypergraph $(V,{\cal F}).$  A pivotal result in the study of positional games is the Erdős–Selfridge theorem, which gives a simple criterion for the existence of a Breaker's winning strategy on a finite hypergraph ${\cal F}$.  It has been shown that the bound in the Erdős–Selfridge theorem can be tight and that numerous extremal hypergraphs exist that demonstrate the tightness of the bound. We focus on a generalization of the Erdős–Selfridge theorem proven by Beck for biased $(p:q)$ games, which we call the $(p:q)$–Erdős–Selfridge theorem.  We show that for $pn$-uniform hypergraphs there is a unique extremal hypergraph for the $(p:q)$–Erdős–Selfridge theorem when $q\geq 2$.

scholarly journals On the Chvátal-Erdős Triangle Game

10.37236/559 ◽  
2011 ◽  
Vol 18 (1) ◽  
Author(s):  
József Balogh ◽  
Wojciech Samotij
Keyword(s):  
Complete Graph ◽  
Winning Strategy ◽  
Seminal Paper ◽  
Positional Games ◽  
Positive Integers

Given a graph $G$ and positive integers $n$ and $q$, let ${\bf G}(G;n,q)$ be the game played on the edges of the complete graph $K_n$ in which the two players, Maker and Breaker, alternately claim $1$ and $q$ edges, respectively. Maker's goal is to occupy all edges in some copy of $G$; Breaker tries to prevent it. In their seminal paper on positional games, Chvátal and Erdős proved that in the game ${\bf G}(K_3;n,q)$, Maker has a winning strategy if $q < \sqrt{2n+2}-5/2$, and if $q \geq 2\sqrt{n}$, then Breaker has a winning strategy. In this note, we improve the latter of these bounds by describing a randomized strategy that allows Breaker to win the game ${\bf G}(K_3;n,q)$ whenever $q \geq (2-1/24)\sqrt{n}$. Moreover, we provide additional evidence supporting the belief that this bound can be further improved to $(\sqrt{2}+o(1))\sqrt{n}$.

On Biased Positional Games

1998 ◽  
Vol 7 (4) ◽  
pp. 339-351 ◽  
Author(s):  
MAŁGORZATA BEDNARSKA
Keyword(s):  
Complete Graph ◽  
Binary Tree ◽  
Winning Strategy ◽  
Positional Games

Let TBin(N, n, q) be the game on the complete graph KN in which two players, the Breaker and the Maker, alternately claim one and q edges, respectively. The Maker's aim is to build a binary tree on n<N vertices in n−1 turns while the Breaker tries to prevent him from doing so. It is shown that, for every constant ε>0, there exists n0 such that, for every n[ges ]n0, the Breaker has a winning strategy in TBin(N, n, q) if q>(1+ε)N/logn, while, for q<(1−ε)N/logn, the game TBin(N, n, q) can be won by the Maker provided that n=o(N).

scholarly journals THE FRONTIER OF DECIDABILITY IN PARTIALLY OBSERVABLE RECURSIVE GAMES

2012 ◽  
Vol 23 (07) ◽  
pp. 1439-1450 ◽  
Author(s):  
DAVID AUGER ◽  
OLIVIER TEYTAUD
Keyword(s):  
Decision Problem ◽  
Winning Strategy ◽  
The Other ◽  
Simple Criterion ◽  
Stochastic Case ◽  
Recursive Games ◽  
Partially Observable ◽  
Random Part ◽  
Classical Decision

The classical decision problem associated with a game is whether a given player has a winning strategy, i.e. some strategy that leads almost surely to a victory, regardless of the other players' strategies. While this problem is relevant for deterministic fully observable games, for a partially observable game the requirement of winning with probability 1 is too strong. In fact, as shown in this paper, a game might be decidable for the simple criterion of almost sure victory, whereas optimal play (even in an approximate sense) is not computable. We therefore propose another criterion, the decidability of which is equivalent to the computability of approximately optimal play. Then, we show that (i) this criterion is undecidable in the general case, even with deterministic games (no random part in the game), (ii) that it is in the jump 0', and that, even in the stochastic case, (iii) it becomes decidable if we add the requirement that the game halts almost surely whatever maybe the strategies of the players.

scholarly journals Biased Positional Games and Small Hypergraphs with Large Covers

10.37236/794 ◽  
2008 ◽  
Vol 15 (1) ◽  
Author(s):  
Michael Krivelevich ◽  
Tibor Szabó
Keyword(s):  
Complete Graph ◽  
Winning Strategy ◽  
Hamilton Cycle ◽  
Covering Number ◽  
New Approach ◽  
Positional Games

We prove that in the biased $(1:b)$ Hamiltonicity and $k$-connectivity Maker-Breaker games ($k>0$ is a constant), played on the edges of the complete graph $K_n$, Maker has a winning strategy for $b\le(\log 2-o(1))n/\log n$. Also, in the biased $(1:b)$ Avoider-Enforcer game played on $E(K_n)$, Enforcer can force Avoider to create a Hamilton cycle when $b\le (1-o(1))n/\log n$. These results are proved using a new approach, relying on the existence of hypergraphs with few edges and large covering number.

Winning the Argument and Moving the Fight: The Legacy of a Grassroots Humanitarian

Public Voices ◽  
2016 ◽  
Vol 14 (1) ◽  
pp. 115
Author(s):  
Mary Coleman
Keyword(s):  
Higher Education ◽  
United States ◽  
Winning Strategy ◽  
Supreme Court Decision ◽  
The United States ◽  
Colleges And Universities ◽  
Lessons Learned ◽  
The Political ◽  
Political Actors ◽  
Trade Offs

The author of this article argues that the two-decades-long litigation struggle was necessary to push the political actors in Mississippi into a more virtuous than vicious legal/political negotiation. The second and related argument, however, is that neither the 1992 United States Supreme Court decision in Fordice nor the negotiation provided an adequate riposte to plaintiffs’ claims. The author shows that their chief counsel for the first phase of the litigation wanted equality of opportunity for historically black colleges and universities (HBCUs), as did the plaintiffs. In the course of explicating the role of a legal grass-roots humanitarian, Coleman suggests lessons learned and trade-offs from that case/negotiation, describing the tradeoffs as part of the political vestiges of legal racism in black public higher education and the need to move HBCUs to a higher level of opportunity at a critical juncture in the life of tuition-dependent colleges and universities in the United States. Throughout the essay the following questions pose themselves: In thinking about the Road to Fordice and to political settlement, would the Justice Department lawyers and the plaintiffs’ lawyers connect at the point of their shared strength? Would the timing of the settlement benefit the plaintiffs and/or the State? Could plaintiffs’ lawyers hold together for the length of the case and move each piece of the case forward in a winning strategy? Who were plaintiffs’ opponents and what was their strategy? With these questions in mind, the author offers an analysis of how the campaign— political/legal arguments and political/legal remedies to remove the vestiges of de jure segregation in higher education—unfolded in Mississippi, with special emphasis on the initiating lawyer in Ayers v. Waller and Fordice, Isaiah Madison

scholarly journals Nanoencapsulated Essential Oils with Enhanced Antifungal Activity for Potential Application on Agri-Food, Material and Environmental Fields

Antibiotics ◽  
2021 ◽  
Vol 10 (1) ◽  
pp. 31
Author(s):  
Magdaléna Kapustová ◽  
Giuseppe Granata ◽  
Edoardo Napoli ◽  
Andrea Puškárová ◽  
Mária Bučková ◽  
...  
Keyword(s):  
Antifungal Activity ◽  
Essential Oil ◽  
Essential Oils ◽  
Winning Strategy ◽  
Colloidal Suspensions ◽  
Fungal Species ◽  
Natural Environments ◽  
Food Material ◽  
Minimum Fungicidal Concentration ◽  
Fungal Strains

Nanotechnology is a new frontier of this century that finds applications in various fields of science with important effects on our life and on the environment. Nanoencapsulation of bioactive compounds is a promising topic of nanotechnology. The excessive use of synthetic compounds with antifungal activity has led to the selection of resistant fungal species. In this context, the use of plant essential oils (EOs) with antifungal activity encapsulated in ecofriendly nanosystems could be a new and winning strategy to overcome the problem. We prepared nanoencapsules containing the essential oils of Origanum vulgare (OV) and Thymus capitatus (TC) by the nanoprecipitation method. The colloidal suspensions were characterized for size, polydispersity index (PDI), zeta potential, efficiency of encapsulation (EE) and loading capacity (LC). Finally, the essential oil nanosuspensions were assayed against a panel of fourteen fungal strains belonging to the Ascomycota and Basidiomycota phyla. Our results show that the nanosystems containing thyme and oregano essential oils were active against various fungal strains from natural environments and materials. In particular, the minimum inhibitory concentration (MIC) and minimum fungicidal concentration (MFC) values were two to four times lower than the pure essential oils. The aqueous, ecofriendly essential oil nanosuspensions with broad-spectrum antifungal activity could be a valid alternative to synthetic products, finding interesting applications in the agri-food and environmental fields.

scholarly journals Rainbow matchings for 3-uniform hypergraphs

2021 ◽  
Vol 183 ◽  
pp. 105489
Author(s):  
Hongliang Lu ◽  
Xingxing Yu ◽  
Xiaofan Yuan
Keyword(s):  
Uniform Hypergraphs

scholarly journals Molecular Identification of Mushroom Species in Italy: An Ongoing Project Aimed at Reinforcing the Control Measures of an Increasingly Appreciated Sustainable Food

2020 ◽  
Vol 13 (1) ◽  
pp. 238
Author(s):  
Alice Giusti ◽  
Enrica Ricci ◽  
Laura Gasperetti ◽  
Marta Galgani ◽  
Luca Polidori ◽  
...  
Keyword(s):  
Selection Process ◽  
Winning Strategy ◽  
Control Measures ◽  
Effective Control ◽  
Mushroom Poisoning ◽  
Clinical Samples ◽  
Similar Species ◽  
Mushroom Species ◽  
Ongoing Research ◽  
Genotypic Analysis

Proper investment in mushroom production (farming and wild mushroom picking activities) may represent a winning strategy for many countries, including Italy, to better face the problems of food security and environmental impact, and to break away from imports, enhancing the local products. However, the risk related to the consumption of poisoning species requires governments to implement or reinforce effective control measures to protect consumers. Mushroom identification by phenotype observation is hardly applicable if morphologically-similar species, non-whole specimens, or clinical samples are involved. Genotypic analysis is a valid alternative. An ongoing research project involving the Experimental Zooprophylactic Institute of Lazio and Tuscany, the regional Mycological Inspectorate, the Tuscany Mycological Groups Association, and the Department of Veterinary Sciences of the University of Pisa aims to reinforce the collaboration among institutions for the management of mushroom poisoning. The core’s project aims to develop an internal genetic database to support the identification of wild and cultivated mushroom species in the Italian territory. The database will include Internal Transcribed Spacer (ITS) sequences retrieved from official databases (the NCBI GenBank and the BOLD system) which are considered to be reliable, after a proper selection process, and sequences from specimens collected directly and identified by expert mycologists. Once it is validated, the database will be available and further implementable by the official network of national laboratories.

scholarly journals Cut-and-Mouse and Ghost Control

2021 ◽  
Vol 2 (1) ◽  
pp. 1-23
Author(s):  
Ziya Alper Genç ◽  
Gabriele Lenzini ◽  
Daniele Sgandurra
Keyword(s):  
Winning Strategy ◽  
Denial Of Service ◽  
Behavioral Analysis ◽  
Full Time ◽  
Standard Code ◽  
Additional Protection ◽  
Protection Mechanisms ◽  
Copy And Paste ◽  
Digital Assets

To protect their digital assets from malware attacks, most users and companies rely on antivirus (AV) software. AVs’ protection is a full-time task against malware: This is similar to a game where malware, e.g., through obfuscation and polymorphism, denial of service attacks, and malformed packets and parameters, tries to circumvent AV defences or make them crash. However, AVs react by complementing signature-based detection with anomaly or behavioral analysis, and by using OS protection, standard code, and binary protection techniques. Further, malware counter-acts, for instance, by using adversarial inputs to avoid detection, and so on. In this cat-and-mouse game, a winning strategy is trying to anticipate the move of the adversary by looking into one’s own weaknesses, seeing how the adversary can penetrate them, and building up appropriate defences or attacks. In this article, we play the role of malware developers and anticipate two novel moves for the malware side to demonstrate the weakness in the AVs and to improve the defences in AVs’ side. The first one consists in simulating mouse events to control AVs, namely, to send them mouse “clicks” to deactivate their protection. We prove that many AVs can be disabled in this way, and we call this class of attacks Ghost Control . The second one consists in controlling whitelisted applications, such as Notepad, by sending them keyboard events (such as “copy-and-paste”) to perform malicious operations on behalf of the malware. We prove that the anti-ransomware protection feature of AVs can be bypassed if we use Notepad as a “puppet” to rewrite the content of protected files as a ransomware would do. Playing with the words, and recalling the cat-and-mouse game, we call this class of attacks Cut-and-Mouse . We tested these two attacks on 29 AVs, and the results show that 14 AVs are vulnerable to Ghost Control attack while all 29 AV programs tested are found vulnerable to Cut-and-Mouse . Furthermore, we also show some weaknesses in additional protection mechanisms of AVs, such as sandboxing and CAPTCHA verification. We have engaged with the affected AV companies, and we reported the disclosure communication with them and their responses.

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