Aspects of quark mass generation on a torus

In this talk we report on recent results for the quark propagator on a compact manifold. The corresponding Dyson-Schwinger equations on a torus are solved on volumes similar to the ones used in lattice calculations. The quark-gluon interaction is fixed such that the lattice results are reproduced. We discuss both the effects in the infinite volume/continuum limit as well as effects when the volume is small.Comment: 3 pages, 3 figures; talk given by CF at QNP06, Madrid, June 200

Even circuits of prescribed clockwise parity

We show that a graph has an orientation under which every circuit of even length is clockwise odd if and only if the graph contains no subgraph which is, after the contraction of at most one circuit of odd length, an even subdivision of K_{2,3}. In fact we give a more general characterisation of graphs that have an orientation under which every even circuit has a prescribed clockwise parity. This problem was motivated by the study of Pfaffian graphs, which are the graphs that have an orientation under which every alternating circuit is clockwise odd. Their significance is that they are precisely the graphs to which Kasteleyn's powerful method for enumerating perfect matchings may be applied

Dynamical Chiral Symmetry Breaking in Landau gauge QCD

We summarise results for the propagators of Landau gauge QCD from the Green's functions approach and lattice calculations. The nonperturbative solutions for the ghost, gluon and quark propagators from a coupled set of Dyson-Schwinger equations agree almost quantitatively with corresponding lattice results. Similar unquenching effects are found in both approaches. The dynamically generated quark masses are close to `phenomenological' values. The chiral condensate is found to be large.Comment: 4 pages, 2 figures, talk given by C.F. at 6th Conference on Quark Confinement and the Hadron Spectrum, Villasimius, Sardinia, Italy, 21-25 Sep 200

Functionally referential signals: a promising paradigm whose time has passed

Finding the evolutionary origins of human language in the communication systems of our closest living relatives has, for the last several decades, been a major goal of many in the field of animal communication generally and primate communication specifically.1–4 The so-called “functionally referential” signals have long been considered promising in this regard, with apparent parallels with the semantic communication that characterizes language. The once-prominent idea that functionally referential signals are word-like, in that they are arbitrary sounds that refer to phenomena external to the caller, has largely been abandoned.5 However, the idea that these signals may offer the strongest link between primate communication and human language remains widespread, primarily due to the fact the behavior of receivers indicates that such signals enable them to make very specific inferences about their physical or social environment. Here we review the concept of functional reference and discuss modern perspectives that indicate that, although the sophistication of receivers provides some continuity between nonhuman primate and human cognition, this continuity is not unique to functionally referential signals. In fact, because functionally referential signals are, by definition, produced only in specific contexts, receivers are less dependent on the integration of contextual cues with signal features to determine an appropriate response. The processing of functionally referential signals is therefore likely to entail simpler cognitive operations than does that of less context-specific signals. While studies of functional reference have been important in highlighting the relatively sophisticated processes that underlie receiver behavior, we believe that the continued focus on context-specific calls detracts from the potentially more complex processes underlying responses to more unspecific calls. In this sense, we argue that the concept of functional reference, while historically important for the field, has outlived its usefulness and become a red herring in the pursuit of the links between primate communication and human language

Endogenous Credit Constraints and Factor Market Rigidities: the case of Bankruptcy

We develop a simple analytical model that highlights the effect of factor rigidities and credit constraints on bankruptcies. In our model, entrepreneurs receive random shocks –positive or negative-- to their working capital, which is needed to pay workers before the output of the firm is sold. If an entrepreneur receives a shock that lowers his working capital sufficiently, she requires loans in order to pay workers and continue operating. However, if the level of working capital is too low, Tirole’s (2000) condition implies the entrepreneur will not receive the necessary loans, due to moral hazard. In this case, the firm must adapt the number of workers to the available funds by firing workers, it is to survive. In the presence of labor rigidities, this may not be possible and the firm goes bankrupt. We show that there are several categories of entrepreneurs, depending on the magnitude of the shock: entrepreneurs who go bankrupt, entrepreneurs that can borrow but not enough to achieve their optimal capital-labor ratio, entrepreneurs that borrow but reach their optimal capital-labor ratio and finally entrepreneurs with that are the creditors in the financial market. We examine the effects of an increase in the labor rigidity on the demand for credit and on the efficiency of the economy. In a second stage, we simulate numerically the costs of these rigidities for sensible parameter values, to estimate bounds to the effects of the interactions between labor rigidity and credit constraints.Credit constraints, rigidities, bankruptcy

Domain formation in membranes with quenched protein obstacles: Lateral heterogeneity and the connection to universality classes

We show that lateral fluidity in membranes containing quenched protein obstacles belongs to the universality class of the two-dimensional random-field Ising model. The main feature of this class is the absence of a phase transition: there is no critical point, and macroscopic domain formation does not occur. Instead, there is only one phase. This phase is highly heterogeneous, with a structure consisting of micro-domains. The presence of quenched protein obstacles thus provides a mechanism to stabilize lipid rafts in equilibrium. Crucial for two-dimensional random-field Ising universality is that the obstacles are randomly distributed, and have a preferred affinity to one of the lipid species. When these conditions are not met, standard Ising or diluted Ising universality apply. In these cases, a critical point does exist, marking the onset toward macroscopic demixing.Comment: 10 pages, 10 figure

Finite volume effects in a quenched lattice-QCD quark propagator

We investigate finite volume effects in the pattern of chiral symmetry breaking. To this end we employ a formulation of the Schwinger-Dyson equations on a torus which reproduces results from the corresponding lattice simulations of staggered quarks and from the overlap action. Studying the volume dependence of the quark propagator we find quantitative differences with the infinite volume result at small momenta and small quark masses. We estimate the minimal box length L below which chiral perturbation theory cannot be applied to be L \simeq 1.6 fm. In the infinite volume limit we find a chiral condensate of ||_{\bar{MS}}^{2 GeV} = (253 \pm 5.0 MeV)^3, an up/down quark mass of m_{\bar{MS}}^{2 GeV} = 4.1 \pm 0.3 MeV and a pion decay constant which is only ten percent smaller than the experimental value.Comment: 19 pages, 8 figures. v2: minor clarifications added, version published in PR