scholarly journals Combinatorial Analysis of a Subtraction Game on Graphs

2016 ◽  
Vol 2016 ◽  
pp. 1-8 ◽  
Author(s):  
Richard Adams ◽  
Janae Dixon ◽  
Jennifer Elder ◽  
Jamie Peabody ◽  
Oscar Vega ◽  
...  
Keyword(s):  
Automorphism Group ◽  
Random Graphs ◽  
The Other ◽  
Combinatorial Analysis ◽  
Combinatorial Game ◽  
Open Question

We define a two-player combinatorial game in which players take alternate turns; each turn consists of deleting a vertex of a graph, together with all the edges containing such vertex. If any vertex became isolated by a player’s move then it would also be deleted. A player wins the game when the other player has no moves available. We study this game under various viewpoints: by finding specific strategies for certain families of graphs, through using properties of a graph’s automorphism group, by writing a program to look at Sprague-Grundy numbers, and by studying the game when played on random graphs. When analyzing Grim played on paths, using the Sprague-Grundy function, we find a connection to a standing open question about Octal games.

Incarnation as Awakening: Katsumi Takizawa Reading Karl Barth

Exchange ◽  
2007 ◽  
Vol 36 (2) ◽  
pp. 144-155
Author(s):  
Susanne Hennecke
Keyword(s):  
Karl Barth ◽  
The Other ◽  
Historical Jesus ◽  
Kyoto School ◽  
Dialectical Theology ◽  
Christian Theologian ◽  
The One ◽  
Open Question

AbstractThis contribution deals with the thinking of the Buddhist philosopher and Christian theologian Katsumi Takizawa (1909-1984) on incarnation. Firstly, it gives a short biographical and theological introduction to Takizawa, who was influenced not only by the "father" of the so-called dialectical theology, Karl Barth, but also by one of the famous figures of the Kyoto-school, the philosopher Kitaro Nishida.This contribution concentrates, secondly, on Takizawa's the-anthropological re-interpretation of the incarnation. It is argued that for Takizawa incarnation has to be seen as an awakening of the historical Jesus (or other historical phenomena) to what he calls the original fact: the eternal relationship between God and man.Thirdly, this contribution discusses the the-anthropological thinking of Takizawa about incarnation in five short points. Apart from the positive challenges of Takizawa's thinking especially for the theology of Karl Barth, it marks clearly the most thrilling point between Takizawa's thinking on the one side and that of scholars in Barthian theology on the other side. The open question that comes up is if incarnation really can be thought without a historical mediation or mediator, as Takizawa seems to claim.

scholarly journals Between 2- and 3-Colorability

10.37236/4673 ◽  
2015 ◽  
Vol 22 (1) ◽  
Author(s):  
Alan Frieze ◽  
Wesley Pegden
Keyword(s):  
Positive Integer ◽  
Random Graphs ◽  
The Other ◽  
Chromatic Numbers ◽  
Other Hand ◽  
Odd Cycles

We consider the question of the existence of homomorphisms between $G_{n,p}$ and odd cycles when $p=c/n$, $1<c\leq 4$. We show that for any positive integer $\ell$, there exists $\epsilon=\epsilon(\ell)$ such that if $c=1+\epsilon$ then w.h.p. $G_{n,p}$ has a homomorphism from $G_{n,p}$ to $C_{2\ell+1}$ so long as its odd-girth is at least $2\ell+1$. On the other hand, we show that if $c=4$ then w.h.p. there is no homomorphism from $G_{n,p}$ to $C_5$. Note that in our range of interest, $\chi(G_{n,p})=3$ w.h.p., implying that there is a homomorphism from $G_{n,p}$ to $C_3$.  These results imply the existence of random graphs with circular chromatic numbers $\chi_c$ satisfying $2<\chi_c(G)<2+\delta$ for arbitrarily small $\delta$, and also that $2.5\leq \chi_c(G_{n,\frac 4 n})<3$ w.h.p.

scholarly journals A SURVEY ON THE AUTOMORPHISM GROUPS OF THE COMMUTING GRAPHS AND POWER GRAPHS

2019 ◽  
pp. 729
Author(s):  
Mahsa Mirzargar
Keyword(s):  
Automorphism Group ◽  
Automorphism Groups ◽  
The Other ◽  
Power Graph ◽  
Commuting Graph ◽  
Vertex Set ◽  
Delta G ◽  
Nite Group

Let G be a nite group. The power graph P(G) of a group G is the graphwhose vertex set is the group elements and two elements are adjacent if one is a power of the other. The commuting graph \Delta(G) of a group G, is the graph whose vertices are the group elements, two of them joined if they commute. When the vertex set is G-Z(G), this graph is denoted by \Gamma(G). Since the results based on the automorphism group of these kinds of graphs are so sporadic, in this paper, we give a survey of all results on the automorphism group of power graphs and commuting graphs obtained in the literature.

scholarly journals PERSISTENCE IN THE ZERO-TEMPERATURE DYNAMICS OF THE Q-STATES POTTS MODEL ON UNDIRECTED-DIRECTED BARABÁSI–ALBERT NETWORKS AND ERDÖS–RÉNYI RANDOM GRAPHS

2008 ◽  
Vol 19 (12) ◽  
pp. 1777-1785 ◽  
Author(s):  
F. P. FERNANDES ◽  
F. W. S. LIMA
Keyword(s):  
Random Graphs ◽  
Potts Model ◽  
Finite Size ◽  
Glauber Dynamics ◽  
The Other ◽  
Finite Size Effect ◽  
Zero Temperature ◽  
Temperature Dynamics ◽  
Short Times ◽  
Q Values

The zero-temperature Glauber dynamics is used to investigate the persistence probability P(t) in the Potts model with Q = 3, 4, 5, 7, 9, 12, 24, 64, 128, 256, 512, 1024, 4096, 16 384, …, 230 states on directed and undirected Barabási–Albert networks and Erdös–Rényi (ER) random graphs. In this model, it is found that P(t) decays exponentially to zero in short times for directed and undirected ER random graphs. For directed and undirected BA networks, in contrast it decays exponentially to a constant value for long times, i.e., P(∞) is different from zero for all Q values (here studied) from Q = 3, 4, 5, …, 230; this shows "blocking" for all these Q values. Except that for Q = 230 in the undirected case P(t) tends exponentially to zero; this could be just a finite-size effect since in the other "blocking" cases you may have only a few unchanged spins.

Framing Engineering Problems: Basic Concept

2014 ◽  
Author(s):  
Shuichi Fukuda
Keyword(s):  
Bounded Rationality ◽  
Basic Concept ◽  
The Other ◽  
Engineering Problems ◽  
Tremendous Amount ◽  
Open Question ◽  
Rational Knowledge

There are two kinds of knowledge in engineering. One is rational knowledge. We understand the phenomena and we can apply rational approaches. The other is knowledge about phenomena which we do not understand well, but which we can control and utilize for engineering. For example, we do not understand arc phenomena well, although there are tremendous amount of work about arc. If we do, we could prevent thunder and lightning. However, we utilize arc for welding. Without arc, most of our bridges, buildings, etc would not have been built. As Engineering is a DO activity and we do not have to UNDERSTAND the phenomena as scientists do. What is very important in engineering is how we can utilize such knowledge about these phenomena, which we do not understand well, but which we can control. And to develop a safe and secure system, we have to let them work in good harmony. This is the problem of frames as AI researchers call it. Although this is still an open question in AI, engineers have to go beyond the bounded rationality. This paper describes the basic concept of how we engineers could possibly tackle this problem.

scholarly journals When is a dynamical system mean sensitive?

2017 ◽  
Vol 39 (06) ◽  
pp. 1608-1636 ◽  
Author(s):  
FELIPE GARCÍA-RAMOS ◽  
JIE LI ◽  
RUIFENG ZHANG
Keyword(s):  
Dynamical System ◽  
Phase Space ◽  
The Other ◽  
Positive Entropy ◽  
Topological Dynamical System ◽  
Other Hand ◽  
Open Question ◽  
Uniquely Ergodic ◽  
Mean Sensitivity ◽  
Transitive System

This article is devoted to studying which conditions imply that a topological dynamical system is mean sensitive and which do not. Among other things, we show that every uniquely ergodic, mixing system with positive entropy is mean sensitive. On the other hand, we provide an example of a transitive system which is cofinitely sensitive or Devaney chaotic with positive entropy but fails to be mean sensitive. As applications of our theory and examples, we negatively answer an open question regarding equicontinuity/sensitivity dichotomies raised by Tu, we introduce and present results of locally mean equicontinuous systems and we show that mean sensitivity of the induced hyperspace does not imply that of the phase space.

scholarly journals IX. Combinatorial analysis. The foundations of a new theory

1900 ◽  
Vol 194 (252-261) ◽  
pp. 361-386 ◽  
Keyword(s):  
General Problem ◽  
Complete Solution ◽  
Latin Square ◽  
The Other ◽  
Combinatorial Analysis ◽  
Great Problem ◽  
Cambridge Philosophical Society ◽  
New Instrument ◽  
Similar Character ◽  
The One

In the ‘Transactions of the Cambridge Philosophical Society’ (vol. 16, Part IV., p. 262), I brought forward a new instrument of research in Combinatorial Analysis, and applied it to the complete solution of the great problem of the “Latin Square,” which had proved a stumbling block to mathematicians since the time of Euler. The method was equally successful in dealing with a general problem of which the Latin Square was but a particular case, and also with many other questions of a similar character. I propose now to submit the method to a close examination, to attempt to establish it firmly, and to ascertain the nature of the questions to which it may be successfully applied. We shall find that it is not merely an enumerating instrument but a powerful reciprocating instrument, from which a host of theorems of algebraical reciprocity can be obtained with facility. We will suppose that combinations defined by certain laws of combination have to be enumerated; the method consists in designing, on the one hand, an operation and, on the other hand, a function in such manner that when the operation is performed upon the function a number results which enumerates the combinations. If this can be carried out we, in general, obtain far more than a single enumeration; we arrive at the point of actually representing graphically all the combinations under enumeration, and solve by the way many other problems which may be regarded as leading up to the problem under consideration. In the case of the Latin Square it was necessary to design the operation and the function the combination of which was competent to yield the solution of the problem. It is a much easier process, and from my present standpoint more scientific, to start by designing the operation and the function, and then to ascertain the questions which the combination is able to deal with.

scholarly journals Egalitarian men: stereotypes and discrimination in the labor market

2020 ◽  
Vol 23 (2) ◽  
pp. 111-147
Author(s):  
Hyalle Abreu Viana ◽  
Ana Raquel Rosas Torres ◽  
José Luis Álvaro Estriamana
Keyword(s):  
Labor Market ◽  
University Students ◽  
Gender Equality ◽  
The Other ◽  
Work Context ◽  
Family Responsibilities ◽  
Men And Women ◽  
Other Hand ◽  
Open Question ◽  
Do So

This article aimed to analyze the stereotypes attributed to "egalitarian men", understood here as men who support gender equality in relation to domestic and family responsibilities as well as inclusion in the workforce. To do so, two studies were carried out. The first study investigated the attribution of stereotypes to egalitarian men through a single open question. A total of 250 university students participated in this study, of which 51.1% were male, and their average age was 21.5 years (SD = 4.39). The second study analyzed the attribution of stereotypes to egalitarian or traditional men and women in a work context considered masculine. Participants included 221 university students with a mean age of 21.9 years (SD = 4.19), the majority (54.3%) being male. Taken together, the results of the two studies indicate that the egalitarian man is perceived as fragile and possibly homosexual. On the other hand, he is also seen as being more competent than traditional men.

scholarly journals A Note on Sparse Random Graphs and Cover Graphs

10.37236/1497 ◽  
2000 ◽  
Vol 7 (1) ◽  
Author(s):  
Tom Bohman ◽  
Alan Frieze ◽  
Miklós Ruszinkó ◽  
Lubos Thoma
Keyword(s):  
Random Graph ◽  
Random Graphs ◽  
High Probability ◽  
The Other ◽  
Other Hand ◽  
Cover Graph

It is shown in this note that with high probability it is enough to destroy all triangles in order to get a cover graph from a random graph $G_{n,p}$ with $p\le \kappa \log n/n$ for any constant $\kappa < 2/3$. On the other hand, this is not true for somewhat higher densities: If $p\ge \lambda (\log n)^3 / (n\log\log n)$ with $\lambda > 1/8$ then with high probability we need to delete more edges than one from every triangle. Our result has a natural algorithmic interpretation.

scholarly journals 0096 Future-Relevant Information is Enhanced After Sleep Despite Emotional Salience of Stimuli

SLEEP ◽  
2020 ◽  
Vol 43 (Supplement_1) ◽  
pp. A38-A39
Author(s):  
L N Whitehurst ◽  
N Sattari ◽  
S C Mednick
Keyword(s):  
Word Pair ◽  
Relevant Information ◽  
The Other ◽  
Sleep Stages ◽  
Naval Research ◽  
False Alarms ◽  
Mental Health Training ◽  
Office Of Naval Research ◽  
Future Events ◽  
Open Question

Abstract Introduction A substantial literature supports that sleep biases memory consolidation and retrieval for emotionally-salient stimuli. A smaller, yet growing, literature supports that information deemed relevant to future events may also be favored by sleep consolidation processes. However, it is unclear whether both emotion and predictability would act together to bias sleep-dependent memory formation. Here, we utilized a directed forgetting paradigm with negative and neutral word pairs to examine this open question. Methods Sixty young and healthy adults were exposed to word pair stimuli before a polysomnographically-recorded nap. Before the nap, participants were instructed to remember half of the word pairs presented for a later test, and for the other half of word pairs, participants were told to forget them as there would not be a test on them later. Additionally, during encoding, half of the subjects in the sample were exposed to negative valenced, high arousal word pairs while the other half were exposed to neutral, low arousal word pairs. After the nap, subjects were tested on all word pairs presented, regardless of previous instruction. This also included a set of novel word pairs to which participants had not been previously exposed. Results A series of 2x2 mixed measures ANOVAs revealed that individuals had better accuracy (p&lt;.001) and fewer misses (p&lt;.001) for the words they were told to remember compared to those they were instructed to forget. Additionally, participants had relatively few false alarms to novel stimuli, 7.14 times, on average (SD=6.10), out of a possible 50 word pairs. Importantly, contrary to predictions, post-nap performance was not dependent on the word pair valence (interaction p’s&gt;.70). No correlations between sleep stages and memory emerged. Conclusion These findings suggest that predictability of future events may be a relevant catalyst for sleep-related memory processing. Support This work was supported by an Office of Naval Research Young Investigators Award to Sara Mednick and a National Institutes of Mental Health Training grant to Lauren Whitehurst T32MH019391.

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