Breaking Symmetries in Graph Representation

There are many complex combinatorial problems which involve searching for an undirected graph satisfying a certain property. These problems are often highly challenging because of the large number of isomorphic representations of a possible solution. In this paper we introduce novel, effective and compact, symmetry breaking constraints for undirected graph search. While incomplete, these prove highly beneficial in pruning the search for a graph. We illustrate the application of symmetry breaking in graph representation to resolve several open instances in extremal graph theory

Optimized generation of spatial qudits by using a pure phase spatial light modulator

We present a method for preparing arbitrary pure states of spatial qudits, namely, D-dimensional (D > 2) quantum systems carrying information in the transverse momentum and position of single photons. For this purpose, a set of D slits with complex transmission are displayed on a spatial light modulator (SLM). In a recent work we have shown a method that requires a single phase-only SLM to control independently the complex coefficients which define the quantum state of dimension D. The amplitude information was codified by introducing phase gratings inside each slit and the phase value of the complex transmission was added to the phase gratings. After a spatial filtering process we obtained in the image plane the desired qudit state. Although this method has proven to be a good alternative to compact the previously reported architectures, it presents some features that could be improved. In this paper we present an alternative scheme to codify the required phase values that minimizes the effects of temporal phase fluctuations associated to the SLM where the codification is carried on. In this scheme the amplitudes are set by appropriate phase gratings addressed at the SLM while the relative phases are obtained by a lateral displacement of these phase gratings. We show that this method improves the quality of the prepared state and provides very high fidelities of preparation for any state. An additional advantage of this scheme is that a complete 2\pi modulation is obtained by shifting the grating by one period, and hence the encoding is not limited by the phase modulation range achieved by the SLM. Numerical simulations, that take into account the phase fluctuations, show high fidelities for thousands of qubit states covering the whole Bloch sphere surface. Similar analysis are performed for qudits with D = 3 and D = 7.Comment: 12 pages, 7 figure

Social partners’ bargaining strategies in Germany and Spain after the introduction of the Euro: a morphogenetic perspective on corporate agency

This article addresses how far wage imbalances in the Eurozone can be imputable to intentional agency by collective bargaining organisations. Using Archer’s morphogenetic approach, we explain the agentic role of social partners in core (Germany) and periphery (Spain) cases, in relation with the respective collective bargaining regimes. We show that the capacity of macro- and meso-level organisations to effect wage-setting practices can be constrained inadvertently by contextual influences with morphostatic properties, generating constrained modes of corporate agency. Yet wage moderation is best understood as a form of agency itself, functioning ‘by being’ rather than ‘doing’, which over time can become more innovative. We contrast this finding with the less constrained capacity of more institutionalized corporate agents, such as transnational business corporations and central state agencies

A model of hyphal tip growth involving microtubule-based transport

We propose a simple model for mass transport within a fungal hypha and its subsequent growth. Inspired by the role of microtubule-transported vesicles, we embody the internal dynamics of mass inside a hypha with mutually excluding particles progressing stochastically along a growing one-dimensional lattice. The connection between long range transport of materials for growth, and the resulting extension of the hyphal tip has not previously been addressed in the modelling literature. We derive and analyse mean-field equations for the model and present a phase diagram of its steady state behaviour, which we compare to simulations. We discuss our results in the context of the filamentous fungus, Neurospora crassa.Comment: 5 pages, 5 figure