Entanglement Enhanced Multiplayer Quantum Games

We investigate the 3-player quantum Prisoner's Dilemma with a certain strategic space, a particular Nash equilibrium that can remove the original dilemma is found. Based on this equilibrium, we show that the game is enhanced by the entanglement of its initial state.Comment: 9 pages, 3 figure

Magic numbers in polymer phase separation -- the importance of being rigid

Cells possess non-membrane-bound bodies, many of which are now understood as phase-separated condensates. One class of such condensates is composed of two polymer species, where each consists of repeated binding sites that interact in a one-to-one fashion with the binding sites of the other polymer. Previous biologically-motivated modeling of such a two-component system surprisingly revealed that phase separation is suppressed for certain combinations of numbers of binding sites. This phenomenon, dubbed the "magic-number effect", occurs if the two polymers can form fully-bonded small oligomers by virtue of the number of binding sites in one polymer being an integer multiple of the number of binding sites of the other. Here we use lattice-model simulations and analytical calculations to show that this magic-number effect can be greatly enhanced if one of the polymer species has a rigid shape that allows for multiple distinct bonding conformations. Moreover, if one species is rigid, the effect is robust over a much greater range of relative concentrations of the two species. Our findings advance our understanding of the fundamental physics of two-component polymer-based phase-separation and suggest implications for biological and synthetic systems.Comment: 8 pages + 15 pages S

Competition of Service Marketplaces: Designing Growth in Service Networks

The cloud computing paradigm gives rise to Web service marketplaces where complex services areprovided by several modular vendors. Recently more and more intermediaries are pushing onto themarket, thereby driving competition. Offering innovative business models which are capable ofattracting service providers and consumers is a reasonable strategy to beat competitors and to takeadvantage of network effects. We develop a mechanism that introduces a novel way of distributingrevenues among service providers – the power ratio. Its underlying presumption is not only tocompensate service providers who actually contribute to a complex service offered at a time, but alsoto pay out partners who are on standby – i.e. vendors that support the network’s variety and stability,but actually do not contribute to the complex service delivered. We show that a payment function thatis based upon the power ratio is a promising approach to draw in service providers as it outperformsa payment function that rewards vendors merely based on their actual allocation in terms of expectedpayoffs for different types of service vendors

Necessary and Sufficient Conditions for Success of the Nuclear Norm Heuristic for Rank Minimization

Minimizing the rank of a matrix subject to constraints is a challenging problem that arises in many applications in control theory, machine learning, and discrete geometry. This class of optimization problems, known as rank minimization, is NP-HARD, and for most practical problems there are no efficient algorithms that yield exact solutions. A popular heuristic algorithm replaces the rank function with the nuclear norm--equal to the sum of the singular values--of the decision variable. In this paper, we provide a necessary and sufficient condition that quantifies when this heuristic successfully finds the minimum rank solution of a linear constraint set. We additionally provide a probability distribution over instances of the affine rank minimization problem such that instances sampled from this distribution satisfy our conditions for success with overwhelming probability provided the number of constraints is appropriately large. Finally, we give empirical evidence that these probabilistic bounds provide accurate predictions of the heuristic's performance in non-asymptotic scenarios.Comment: 21 pages, 3 figures. A short version of this paper will appear at the 47th IEEE Conference on Decision and Contro