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As a starting point for analyzing the price of anarchy, Koutsoupias and Papadimitriou considered a very simple weighted network congestion game, now known as the KP model Here, the network consists of a single source and a single destination (in other words, it is a single-commodity network) that are connected together by parallel links The load on a link is the total weight of players assigned to this link Associated with each link is a capacity (or speed) representing the rate at which the link processes load Each of the players sel shly routes from the source to the destination by using a probability distribution over the links The private objective function of a player is its expected latency The social cost is the expected maximum latency on a link, where the expectation is taken over all random choices of the players Fotakis et al.

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[34] have proved that computing social cost (in the form of expected maximum) is a #P-complete problem The stem of this negative result is the nature of exponential enumeration explicit in the de nition of social cost (as an exponentialsize expectation sum) An essentially identical #P-hardness result has been proven recently by Daskalakis et al [19] This is one of the very few hard enumeration problems known in algorithmic game theory as of today Determining more remains a great challenge Mavronicolas and Spirakis [69] introduced fully mixed Nash equilibria for the particular case of the KP model, in which each player chooses every link with positive probability Gairing et al [38,39] explicitly conjectured that, in case the fully mixed Nash equilibrium exists, it is the worst-case Nash equilibrium with respect to social cost This so-called fully mixed Nash equilibrium conjecture is simultaneously intuitive and signi cant.

Dispersal Mechanism Wind Water Bird Animal References 25 + + + + + + + + + + + + + + + + + + + + + + + + 10 10 10 50 35 15 25 35 25 20 5 25 15 20 + + + + + + + + + + + + Schneider and Sharitz, 1988 Middleton, 2000 Schneider and Sharitz, 1988; Haynes and Moore, 1988 Brewer, 1998 Haynes and Moore, 1988 Haynes et al., 1988 Haynes and Moore, 1988 Haynes and Moore, 1988 Haynes and Moore, 1988 Haynes and Moore, 1988 Morris, 1965; Middleton, 2000; Haynes and Moore, 1988 Haynes and Moore, 1988 Haynes and Moore, 1988 Haynes and Moore, 1988 Haynes and Moore, 1988 Haynes and Moore, 1988 Haynes and Moore, 1988 Haynes and Moore, 1988

It is intuitive because the fully mixed Nash equilibrium favors an increased number of collisions between different players, since each player assigns its load with positive probability to every link This increased probability of collisions should favor an increase to social cost The conjecture is also signi cant since it identi es the worst-case Nash equilibrium over all instances The fully mixed Nash equilibrium conjecture has been studied very intensively in the last few years over a variety of settings and models relative to the KP model The KP model was recently extended to restricted strategy sets [9,35], where the strategy set of each player is a subset of the links Furthermore, the KP model was.

Here, NH+, RNH+, R2NH+, R3NH+ and PyH+ (R: alkyl; Py: pyridine) are examples 4 3 2 of BH+-type acids. An acid (HA or BH+), with an intrinsically strong proton donor capacity, completely dissociates in water and forms its conjugate base (A or B) and H3O+. Practically, HA or BH+ do not remain in the solution. This acid is called a strong acid. Examples of strong acids in water are hydrochloric, nitric and perchloric acids. The hydronium ion (H3O+) is the strongest acid that can remain in water. The strengths of the acids, which are stronger than H3O+, cannot be differentiated and are equivalent to the strength of H3O+. This phenomenon is called the leveling effect. For acids that are weaker than H3O+, the reactions in Eqs (3.1) or (3.2) proceed only partially to the right. These acids are called weak acids and their acid strengths are measured by the values of the acid dissociation constant defined by Eqs (3.3) or (3.4): Ka Ka a H3 O a A c2 H3 O A a HA HA a H3 O a B H3 O B a BH BH 3:3 3:4

For diabetic patients there is no such thing as subclinical or subthreshold eating disorders. It is necessary to screen the diabetic population, especially young and adolescent females for eating pathology. If possible, the high risk population should be subjected to a psychiatric interview. A useful rst step might be intensi ed contact with a dietician, followed by psychotherapeutic contact if necessary. Close liaison between psychotherapist and diabetes team is essential, as well as a basic understanding of management of diabetes on the therapist s part.

An electrolytic cell (left) and an electron transfer reaction at the electrode (right). E1, working or indicator electrode, at which the reaction under study occurs; E2, counter electrode with a constant potential; A, current measuring device; V, voltage measuring device.