Decompositions of complete tripartite graphs into triangles with an edge attached

Let K(r, s, t) denote the complete tripartite graph with partite sets of size r, s and t, where r less than or equal to s less than or equal to t. Let D be the graph consisting of a triangle with an edge attached. We show that K(r, s, t) may be decomposed into copies of D if and only if 4 divides rs + st + rt and t less than or equal to 3rs/(r + s).

Bright tripartite entanglement in triply concurrent parametric oscillation

We show that an optical parametric oscillator based on three concurrent chi((2)) nonlinearities can produce, above threshold, bright output beams of macroscopic intensities which exhibit strong tripartite continuous-variable entanglement. We also show that there are two ways that the system can exhibit a three-mode form of the Einstein-Podolsky-Rosen paradox, and calculate the extracavity fluctuation spectra that may be measured to verify our predictions.

Continuous variable tripartite entanglement and Einstein-Podolsky-Rosen correlations from triple nonlinearities

We compare theoretically the tripartite entanglement available from the use of three concurrent x(2) nonlinearities and three independent squeezed states mixed on beamsplitters, using an appropriate version of the van Loock-Furusawa inequalities. We also define three-mode generalizations of the Einstein-Podolsky-Rosen paradox which are an alternative for demonstrating the inseparability of the density matrix.

Continuous variable tripartite entanglement from twin nonlinearities

In this work, we analyse and compare the continuous variable tripartite entanglement available from the use of two concurrent or cascaded X (2) nonlinearities. We examine both idealized travelling-wave models and more experimentally realistic intracavity models, showing that tripartite entangled outputs are readily producible. These may be a useful resource for applications such as quantum cryptography and teleportation.

Long-run effects of unfunded social security with earnings-dependent benefits

This paper examines the effects of unfunded social security with bequests, fertility and human capital by considering a mix of earnings-dependent and universal social security benefits. We show that social security is more likely to promote growth by reducing fertility and increasing human capital investment if its benefits are more dependent on individuals' own earnings. Through simulations, we find that the differences in the effects of social security resulting from variations in the benefit formula can be too substantial to be ignored. We also investigate the welfare effect in calibrated economies. (C) 2003 Elsevier B.V. All rights reserved.

Cleaner fish use tactile dancing behavior as a preconflict management strategy

The most commonly asked question about cooperative interactions is how they are maintained when cheating is theoretically more profitable [1]. In cleaning interactions, where cleaners remove parasites from apparently cooperating clients, the classical question asked is why cleaner fish can clean piscivorous client fish without being eaten, a problem Trivers [2] used to explain reciprocal altruism. Trivers [2] suggested that predators refrain from eating cleaners only when the repeated removal of parasites by a particular cleaner results in a greater benefit than eating the cleaner. Although several theoretical models have examined cheating behavior in clients [3,4], no empirical tests have been done (but see Darcy [5]). It has been observed that cleaners are susceptible to predation [6, 7]. Thus, cleaners should have evolved strategies to avoid conflict or being eaten. In primates, conflicts are often resolved with conflict or preconflict management behavior [8]. Here, I show that cleaner fish tactically stimulate clients while swimming in an oscillating dancing manner (tactile dancing) more when exposed to hungry piscivorous clients than satiated ones, regardless of the client's parasite load. Tactile dancing thus may function as a preconflict management strategy that enables cleaner fish to avoid conflict with potentially dangerous clients.

Critical fluctuations and entanglement in the nondegenerate parametric oscillator

We present a fully quantum mechanical treatment of the nondegenerate optical parametric oscillator both below and near threshold. This is a nonequilibrium quantum system with a critical point phase transition, that is also known to exhibit strong yet easily observed squeezing and quantum entanglement. Our treatment makes use of the positive P representation and goes beyond the usual linearized theory. We compare our analytical results with numerical simulations and find excellent agreement. We also carry out a detailed comparison of our results with those obtained from stochastic electrodynamics, a theory obtained by truncating the equation of motion for the Wigner function, with a view to locating regions of agreement and disagreement between the two. We calculate commonly used measures of quantum behavior including entanglement, squeezing, and Einstein-Podolsky-Rosen (EPR) correlations as well as higher order tripartite correlations, and show how these are modified as the critical point is approached. These results are compared with those obtained using two degenerate parametric oscillators, and we find that in the near-critical region the nondegenerate oscillator has stronger EPR correlations. In general, the critical fluctuations represent an ultimate limit to the possible entanglement that can be achieved in a nondegenerate parametric oscillator.

Continuous-variable quantum-state sharing via quantum disentanglement

Quantum-state sharing is a protocol where perfect reconstruction of quantum states is achieved with incomplete or partial information in a multipartite quantum network. Quantum-state sharing allows for secure communication in a quantum network where partial information is lost or acquired by malicious parties. This protocol utilizes entanglement for the secret-state distribution and a class of quantum disentangling protocols for the state reconstruction. We demonstrate a quantum-state sharing protocol in which a tripartite entangled state is used to encode and distribute a secret state to three players. Any two of these players can collaborate to reconstruct the secret state, while individual players obtain no information. We investigate a number of quantum disentangling processes and experimentally demonstrate quantum-state reconstruction using two of these protocols. We experimentally measure a fidelity, averaged over all reconstruction permutations, of F=0.73 +/- 0.02. A result achievable only by using quantum resources.

Factor structure of the Mood and Anxiety Symptom Questionnaire does not generalize to an anxious/depressed sample

Objective: The tripartite model of anxiety and depression has been proposed as a representation of the structure of anxiety and depression symptoms. The Mood and Anxiety Symptom Questionnaire (MASQ) has been put forwards as a valid measure of the tripartite model of anxiety and depression symptoms. This research set out to examine the factor structure of anxiety and depression symptoms in a clinical sample to assess the MASQ's validity for use in this population. MethodsThe present study uses confirmatory factor analytic methods to examine the psychometric properties of the MASQ in 470 outpatients with anxiety and mood disorder. Results: The results showed that none of the previously reported two-factor, three-factor or five-factor models adequately fit the data, irrespective of whether items or subscales were used as the unit of analysis. Conclusions: It was concluded that the factor structure of the MASQ in a mixed anxiety/depression clinical sample does not support a structure consistent with the tripartite model. This suggests that researchers using the MASQ with anxious/depressed individuals should be mindful of the instrument's psychometric limitations.

Image scoring and cooperation in a cleaner fish mutualism

Humans are highly social animals and often help unrelated individuals that may never reciprocate the altruist's favour(1-5). This apparent evolutionary puzzle may be explained by the altruist's gain in social image: image-scoring bystanders, also known as eavesdroppers, notice the altruistic act and therefore are more likely to help the altruist in the future(5-7). Such complex indirect reciprocity based on altruistic acts may evolve only after simple indirect reciprocity has been established, which requires two steps. First, image scoring evolves when bystanders gain personal benefits from information gathered, for example, by finding cooperative partners(8-10). Second, altruistic behaviour in the presence of such bystanders may evolve if altruists benefit from access to the bystanders. Here, we provide experimental evidence for both of the requirements in a cleaning mutualism involving the cleaner fish Labroides dimidiatus. These cleaners may cooperate and remove ectoparasites from clients or they may cheat by feeding on client mucus(11,12). As mucus may be preferred over typical client ectoparasites(13), clients must make cleaners feed against their preference to obtain a cooperative service. We found that eavesdropping clients spent more time next to 'cooperative' than 'unknown cooperative level' cleaners, which shows that clients engage in image-scoring behaviour. Furthermore, trained cleaners learned to feed more cooperatively when in an `image-scoring' than in a 'non-image-scoring' situation.