Rendezvous search on a graph

1999 ◽  
Vol 36 (1) ◽  
pp. 223-231 ◽  
Author(s):  
Steve Alpern ◽  
V. J. Baston ◽  
Skander Essegaier
Keyword(s):  
Complete Graph ◽  
Continuous Time ◽  
The Other ◽  
Spatial Uncertainty ◽  
Mixed Strategies ◽  
Expected Number ◽  
Time And Space ◽  
Two Agents ◽  
Adjacent Node ◽  
Initial Placement

Two agents are placed randomly on nodes of a known graph. They are aware of their own position, up to certain symmetries of the graph, but not that of the other agent. At each step, each agent may stay where he is or move to an adjacent node. Their common aim is to minimize the expected number of steps required to meet (occupy the same node). We consider two cases determined by whether or not the players are constrained to use identical strategies. This work extends that of Anderson and Weber on ‘discrete locations’ (complete graph) and is related to continuous (time and space) rendezvous as formulated by Alpern. Probabilistic notions arise in the random initial placement, in the random symmetries determining spatial uncertainty of agents, and through the use of mixed strategies.

Rendezvous search on a graph

1999 ◽  
Vol 36 (01) ◽  
pp. 223-231 ◽  
Author(s):  
Steve Alpern ◽  
V. J. Baston ◽  
Skander Essegaier
Keyword(s):  
Complete Graph ◽  
Continuous Time ◽  
The Other ◽  
Spatial Uncertainty ◽  
Mixed Strategies ◽  
Expected Number ◽  
Time And Space ◽  
Two Agents ◽  
Adjacent Node ◽  
Initial Placement

Two agents are placed randomly on nodes of a known graph. They are aware of their own position, up to certain symmetries of the graph, but not that of the other agent. At each step, each agent may stay where he is or move to an adjacent node. Their common aim is to minimize the expected number of steps required to meet (occupy the same node). We consider two cases determined by whether or not the players are constrained to use identical strategies. This work extends that of Anderson and Weber on ‘discrete locations’ (complete graph) and is related to continuous (time and space) rendezvous as formulated by Alpern. Probabilistic notions arise in the random initial placement, in the random symmetries determining spatial uncertainty of agents, and through the use of mixed strategies.

scholarly journals Weak Berge Equilibrium in Finite Three-person Games: Conception and Computation

2020 ◽  
Vol 11 (1) ◽  
pp. 127-134
Author(s):  
Konstantin Kudryavtsev ◽  
Ustav Malkov
Keyword(s):  
Cooperative Games ◽  
Hippocratic Oath ◽  
The Other ◽  
Mixed Strategies ◽  
Finite Games ◽  
Moral Basis ◽  
Other Hand ◽  
Berge Equilibrium ◽  
Do No Harm ◽  
Non Cooperative Games

AbstractThe paper proposes the concept of a weak Berge equilibrium. Unlike the Berge equilibrium, the moral basis of this equilibrium is the Hippocratic Oath “First do no harm”. On the other hand, any Berge equilibrium is a weak Berge equilibrium. But, there are weak Berge equilibria, which are not the Berge equilibria. The properties of the weak Berge equilibrium have been investigated. The existence of the weak Berge equilibrium in mixed strategies has been established for finite games. The weak Berge equilibria for finite three-person non-cooperative games are computed.

scholarly journals What Is Orientation in Dignitarian Thinking? Self, Other, Time and Space

2020 ◽  
pp. 174387212098228
Author(s):  
Stephen Riley
Keyword(s):  
The Self ◽  
The Other ◽  
Core Area ◽  
Methodological Challenge ◽  
Time And Space ◽  
Normative Discourse ◽  
The Government

Drawing upon Kant’s analysis of the role of intuitions in our orientation towards knowledge, this paper analyses four points of departure in thinking about dignity: self, other, time and space. Each reveals a core area of normative discourse – authenticity in the self, respect for the other, progress through time and authority as the government of space – along with related grounds of resistance to dignity. The paper concludes with a discussion of the methodological challenge presented by our different dignitarian intuitions, in particular the role of universality in testing and cohering our intuitions.

Spatial and Temporal Overlap of the American Lobster (Homarus americanus) and Sea Scallop (Placopecten magellanicus) as Related to the impact of Inshore Scallop Dragging

1992 ◽  
Vol 49 (7) ◽  
pp. 1486-1492 ◽  
Author(s):  
D. L. Roddick ◽  
R. J. Miller
Keyword(s):  
Nova Scotia ◽  
Homarus Americanus ◽  
Fishing Effort ◽  
The Other ◽  
American Lobster ◽  
Placopecten Magellanicus ◽  
Time And Space ◽  
Sea Scallop ◽  
The Impact ◽  
Temporal Overlap

Assessment of the damage of one fishery by another requires knowledge of the overlap, in time and space, of the damaging fishing effort and the abundance of the damaged species, as well as a measure of the rate of damage. This approach was used to measure the impact of inshore scallop dragging on lobsters in Nova Scotia. Areas of reported co-occurrence of lobster and scallop grounds were surveyed by divers to determine the extent of overlap. Only 2 of 52 sites surveyed had lobsters on scallop grounds that could be dragged. Divers surveyed one site six times during 1987 and 1988 and found lobsters most abundant during August and September. Only 2% of the lobsters in the path of scallop drags were either captured or injured. The estimated value of lobsters destroyed by dragging for scallops during periods of peak lobster abundance was minor: $757 at one site and $176 at the other. Restricting dragging to periods of low lobster abundance significantly reduces this cost.

Is There a Place for Anthropology in Social Science History?

1999 ◽  
Vol 23 (4) ◽  
pp. 535-559
Author(s):  
Alice Bee Kasakoff
Keyword(s):  
Social Science ◽  
The Other ◽  
One Dimension ◽  
Time And Space ◽  
Science History ◽  
Social Science History ◽  
Secure Place

Imagine a fourfold table in which one dimension is “present versus past” and the other “exotic versus home.” Traditionally, social and cultural anthropology’s domain has been the exotic’s present and history’s domain the home’s past. A third box, the home’s present, has been occupied by sociology, while the fourth, the exotic’s past, has usually been the province of anthropologists too because other disciplines—with the exception, perhaps, of ethnohistorians—are usually even less interested in exotic peoples’ past than in their present. These domains are now in flux. I argue, in what follows, that only when the oversimplified ideas about time and space that have created them are seriously questioned will anthropology find a secure “place” in social science history.

III.—On the Distribution of the Graptolithidæ in Time and Space

1885 ◽  
Vol 2 (9) ◽  
pp. 406-412
Author(s):  
Otto Herrmann
Keyword(s):  
The Other ◽  
New Genera ◽  
Time And Space ◽  
Subsequent Investigation ◽  
Single Genus

It was indicated even by Murchison that the Graptolites constitute admirable characteristic fossils of the Silurian formation. Subsequent investigation has established that the group Graptolithidæ is essentially confined to the oldest fossiliferous formation. A single genus, the genus Dictyograptus, Hopk. (Dictyonema, Hall), occupies a remarkably exceptional position as regards its distribution in time. Formerly, indeed, this genus was separated from the proper or true Graptolites (Rhabdophora, Allman), and referred with some other genera (Dendrograptus, Hall, Ptilograptus, Hopk., Callogroptus, Hall) to the Campanularidæ but recently W. C. Brögger has very clearly shown that the genus in question differs very little from the true Graptolites, inasmuch as the most important parts of the latter, such as the sicula, and the hydrothecæ, have been detected in it. By this the Graptolithic nature of the genus in question is rendered very probable. Members of the genus Dictyograptus, Hopk., appear among the very oldest of known Graptolites; the genus maintains itself throughout the whole of the Silurian formation, while by its side new genera make their appearance, culminate and disappear. Even after the other Graptolites had long since disappeared from the ancient sea-fauna, this genus still lived on, for we find it occurring in the Devonian.

COMPUTING THE RUPTURE DEGREE IN COMPOSITE GRAPHS

2010 ◽  
Vol 21 (03) ◽  
pp. 311-319 ◽  
Author(s):  
AYSUN AYTAC ◽  
ZEYNEP NIHAN ODABAS
Keyword(s):  
Complete Graph ◽  
Connected Graph ◽  
The Other ◽  
Trade Off ◽  
Number Of Components ◽  
Np Complete ◽  
Work Done ◽  
Better Than

The rupture degree of an incomplete connected graph G is defined by [Formula: see text] where w(G - S) is the number of components of G - S and m(G - S) is the order of a largest component of G - S. For the complete graph Kn, rupture degree is defined as 1 - n. This parameter can be used to measure the vulnerability of a graph. Rupture degree can reflect the vulnerability of graphs better than or independent of the other parameters. To some extent, it represents a trade-off between the amount of work done to damage the network and how badly the network is damaged. Computing the rupture degree of a graph is NP-complete. In this paper, we give formulas for the rupture degree of composition of some special graphs and we consider the relationships between the rupture degree and other vulnerability parameters.

scholarly journals ON THE CONSENSUS THRESHOLD FOR THE OPINION DYNAMICS OF KRAUSE–HEGSELMANN

2005 ◽  
Vol 16 (02) ◽  
pp. 259-270 ◽  
Author(s):  
SANTO FORTUNATO
Keyword(s):  
Social Relationships ◽  
Complete Graph ◽  
Opinion Dynamics ◽  
Consensus Model ◽  
Confidence Bound ◽  
Real Numbers ◽  
Numerical Evidence ◽  
Two Agents ◽  
The Social ◽  
The Difference

In the consensus model of Krause–Hegselmann, opinions are real numbers between 0 and 1, and two agents are compatible if the difference of their opinions is smaller than the confidence bound parameter ∊. A randomly chosen agent takes the average of the opinions of all neighboring agents which are compatible with it. We propose a conjecture, based on numerical evidence, on the value of the consensus threshold ∊c of this model. We claim that ∊c can take only two possible values, depending on the behavior of the average degree d of the graph representing the social relationships, when the population N approaches infinity: if d diverges when N→∞, ∊c equals the consensus threshold ∊i~0.2 on the complete graph; if instead d stays finite when N→∞, ∊c =1/2 as for the model of Deffuant et al.

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