Ensuring the boundedness of the core of games with restricted cooperation

The core of a cooperative game on a set of players N is one of the most popular concept of solution. When cooperation is restricted (feasible coalitions form a subcollection F of 2N), the core may become unbounded, which makes it usage questionable in practice. Our proposal is to make the core bounded by turning some of the inequalities defining the core into equalities (additional efficiency constraints). We address the following mathematical problem : can we find a minimal set of inequalities in the core such that, if turned into equalities, the core becomes bounded ? The new core obtained is called the restricted core. We completely solve the question when F is a distributive lattice, introducing also the notion of restricted Weber set. We show that the case of regular set systems amounts more or less to the case of distributive lattices. We also study the case of weakly union-closed systems and give some results for the general case.Cooperative game, core, restricted cooperation, bounded core, Weber set.

Capacities of Grassmann channels

A new class of quantum channels called Grassmann channels is introduced and their classical and quantum capacity is calculated. The channel class appears in a study of the two-mode squeezing operator constructed from operators satisfying the fermionic algebra. We compare Grassmann channels with the channels induced by the bosonic two-mode squeezing operator. Among other results, we challenge the relevance of calculating entanglement measures to assess or compare the ability of bosonic and fermionic states to send quantum information to uniformly accelerated frames.Comment: 33 pages, Accepted in Journal of Mathematical Physics; The role of the (fermionic) braided tensor product for quantum Shannon theory, namely capacity formulas, elucidated; The conclusion on the equivalence of Unruh effect for bosons and fermions for quantum communication purposes made clear and even more precis

Making sense of assets: Community asset mapping and related approaches for cultivating capacities

This working paper critically reviews some main aspects from asset based approaches highlights key strengths and weaknesses for future research/development. Drawing on a large body of reports and relevant literature we draw on different theoretical traditions and critiques, as well as practices and processes embedded within a broad range of approaches including, widely acknowledged frameworks such Asset Based Community Development (ABCD), Appreciative Inquiry (AI), Sustainable Livelihood Approaches (SLA) and Community Capitals Framework (CCF). Although these are presented as distinct approaches, there is a sense of evolution through them and many of them overlap (in terms of both theories and methodologies). We also include emerging frameworks, including geographical, socio-spatial, visual and creative approaches, stemming from a number of projects within AHRC’s Connected Communities programme and additional collaborations

Information-theoretical meaning of quantum dynamical entropy

The theory of noncommutative dynamical entropy and quantum symbolic dynamics for quantum dynamical systems is analised from the point of view of quantum information theory. Using a general quantum dynamical system as a communication channel one can define different classical capacities depending on the character of resources applied for encoding and decoding procedures and on the type of information sources. It is shown that for Bernoulli sources the entanglement-assisted classical capacity, which is the largest one, is bounded from above by the quantum dynamical entropy defined in terms of operational partitions of unity. Stronger results are proved for the particular class of quantum dynamical systems -- quantum Bernoulli shifts. Different classical capacities are exactly computed and the entanglement-assisted one is equal to the dynamical entropy in this case.Comment: 6 page

The Fourth Law of Black Hole Thermodynamics

We show that black holes fulfill the scaling laws arising in critical transitions. In particular, we find that in the transition from negative to positive values the heat capacities $C_{JQ}$, $C_{\Omega Q}$ and $C_{J\Phi}$ give rise to critical exponents satisfying the scaling laws. The three transitions have the same critical exponents as predicted by the universality Hypothesis. We also briefly discuss the implications of this result with regards to the connections among gravitation, quantum mechanics and statistical physics.Comment: 19 pages (two figures), Plain Tex. Preprint KONS-RGKU-93-11. To appear in Nucl. Phys. B (1993

Distributed implementation of standard oracle operators

The standard oracle operator corresponding to a function f is a unitary operator that computes this function coherently, i.e. it maintains superpositions. This operator acts on a bipartite system, where the subsystems are the input and output registers. In distributed quantum computation, these subsystems may be spatially separated, in which case we will be interested in its classical and entangling capacities. For an arbitrary function f, we show that the unidirectional classical and entangling capacities of this operator are log_{2}(n_{f}) bits/ebits, where n_{f} is the number of different values this function can take. An optimal procedure for bidirectional classical communication with a standard oracle operator corresponding to a permutation on Z_{M} is given. The bidirectional classical capacity of such an operator is found to be 2log_{2}(M) bits. The proofs of these capacities are facilitated by an optimal distributed protocol for the implementation of an arbitrary standard oracle operator.Comment: 4.4 pages, Revtex 4. Submitted to Physical Review Letter

Fairness in Multiuser Systems with Polymatroid Capacity Region

For a wide class of multi-user systems, a subset of capacity region which includes the corner points and the sum-capacity facet has a special structure known as polymatroid. Multiaccess channels with fixed input distributions and multiple-antenna broadcast channels are examples of such systems. Any interior point of the sum-capacity facet can be achieved by time-sharing among corner points or by an alternative method known as rate-splitting. The main purpose of this paper is to find a point on the sum-capacity facet which satisfies a notion of fairness among active users. This problem is addressed in two cases: (i) where the complexity of achieving interior points is not feasible, and (ii) where the complexity of achieving interior points is feasible. For the first case, the corner point for which the minimum rate of the active users is maximized (max-min corner point) is desired for signaling. A simple greedy algorithm is introduced to find the optimum max-min corner point. For the second case, the polymatroid properties are exploited to locate a rate-vector on the sum-capacity facet which is optimally fair in the sense that the minimum rate among all users is maximized (max-min rate). In the case that the rate of some users can not increase further (attain the max-min value), the algorithm recursively maximizes the minimum rate among the rest of the users. It is shown that the problems of deriving the time-sharing coefficients or rate-spitting scheme can be solved by decomposing the problem to some lower-dimensional subproblems. In addition, a fast algorithm to compute the time-sharing coefficients to attain a general point on the sum-capacity facet is proposed.Comment: Submitted To IEEE Transactions on Information Theory, June 200