Joan E. Donoghue\u27s theories regarding the prospects for a convention on foreign state immunity within the Hague Conference are examined. The prospects for supporting efforts to negotiate an international convention on state immunity are small

Mårtensson, Christopher

Sjövall, Linus

English

Robertson, Horace B., Jr.

Duke Law Scholarship Repository

Comments of Professor Joan E. Donoghue’s Article, the Public Face of Private International Law: Prospects for a Convention on Foreign State Immunity

An interesting eld of mathematics is the study of swarming and ocking. By using graph theory, one can describe a system of agents that transfer information between each other. With the help of certain algorithms it is possible to update the agent's information in order to reach consensus between the agents. If the information relates to the position, the velocity, or the acceleration of each agent, a behaviour similar to that of animals ocks or insect swarms is observed. Several other applications also exist, for example in systems of multiple robots when no central coordination is possible or simply not desired. In this paper dierent algorithms used to change the agent's information state will be studied and researched in order to determine the requirements under which the entire set of agents achieve consensus. First the case where agents receive information from a non-changing set of agents will be studied. Specically a particular algorithm, where each agent's information is determined by a linear function depending on the information state of all other agents from which information is received, will be considered. A requirement for this particular algorithm to reach consensus is that every agent both receives information and also sends information to every other agent, directly or indirectly through other agents. If all information transfers are weighed equally, the consensus achieved will be the average of all initial information states. Consensus can also be reached under looser conditions where there exists an agent that sends information to every other agent, directly or indirectly. The changes of the system's behaviour when one uses dierent consensus algorithms will be discussed, and computer simulations of these will be provided. An interesting case is where the information (often referring to location, velocity or acceleration) is received only from agents within a given distance and thus the information is received from dierent agents at dierent times. This results in nonlinear algorithms and mostly simulations and interpretations will be given. An observation is that whether consensus is achieved or not depends partially on the initial information states of the agents and the maximum distance for information transfer.Ett intressant omrade inom matematiken ar att beskriva fenomenet med ockar och svarmar. Med hjalp av grafteori kan man beskriva ett system av agenter som skickar information mellan varandra och med hjalp av algoritmer som beskriver hur varje agents informationen ska uppdateras sa att konsensus nas. Om informationen beskriver en position eller foryttning i rummet kan man observera ett beteende som liknar det hos djurockar eller insektssv armar. Manga andra tillampningsomraden nns ocksa, till exempel i system av robotar nar det saknas central styrning och internt beslutstagande ar onskvart. I denna rapport kommer olika algoritmer for att uppdatera en agents status att undersokas for att bestamma vilka krav som nns for att konsensus skall nas. Forsta delen kommer att behandla ett enklare fall dar varje agent tar emot information fran en oforanderlig uppsattning agenter. Specikt sa kommer en algoritm, dar en agents status bestams av en linjar funktion som beror pa statusen hos de agenter fran vilka information mottages, att studeras. Ett krav for att denna algoritm ska na konsensus ar att varje agent bade skickar och tar emot information fran samtliga ovriga agenter, direkt eller indirekt via andra agenter. Om alla informations overforingar vags lika sa kommer alla agenter na medelvardet av agenternas initialvarden. Konsensus kan ocksa nas under mindre restriktiva villkor, om det nns en agent som skickar information till alla andra noder (direkt eller indirekt). Forandringar av systemets beteende vid olika uppdateringsalgoritmer kommer att studeras och datorsimuleringar av dessa fenomen kommer att ges. Ett intressant fall ar da informationen (ofta position, hastighet eller acceleration) endast kan tas emot fran de agenter som nns inom ett givet avstand. darmed forandras den uppsattning agenter med vilka information overfors med tiden. Detta resulterar i olinjara algoritmer och framforallt kommer simulationer och tolkningar av dessa att ges. En observation ar att om konsensus nas eller inte beror starkt pa densiteten bland agenterna i utgangslaget samt det maximala avstand vid vilket informationsoverforing kan ske

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Consensus Algorithms - Flocking and Swarms.

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Comments of Professor Joan E. Donoghue’s Article, the Public Face of Private International Law: Prospects for a Convention on Foreign State Immunity

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