Chirally symmetric quark description of low energy \pi-\pi scattering

Weinberg's theorem for \pi-\pi scattering, including the Adler zero at threshold in the chiral limit, is analytically proved for microscopic quark models that preserve chiral symmetry. Implementing Ward-Takahashi identities, the isospin 0 and 2 scattering lengths are derived in exact agreement with Weinberg's low energy results. Our proof applies to alternative quark formulations including the Hamiltonian and Euclidean space Dyson-Schwinger approaches. Finally, the threshold \pi-\pi scattering amplitudes are calculated using the Dyson-Schwinger equations in the rainbow-ladder truncation, confirming the formal derivation.Comment: 10 pages, 7 figures, Revtex

A statistical mechanics description of environmental variability in metabolic networks

Many of the chemical reactions that take place within a living cell are irreversible. Due to evolutionary pressures, the number of allowable reactions within these systems are highly constrained and thus the resulting metabolic networks display considerable asymmetry. In this paper, we explore possible evolutionary factors pertaining to the reduced symmetry observed in these networks, and demonstrate the important role environmental variability plays in shaping their structural organization. Interpreting the returnability index as an equilibrium constant for a reaction network in equilibrium with a hypothetical reference system, enables us to quantify the extent to which a metabolic network is in disequilibrium. Further, by introducing a new directed centrality measure via an extension of the subgraph centrality metric to directed networks, we are able to characterise individual metabolites by their participation within metabolic pathways. To demonstrate these ideas, we study 116 metabolic networks of bacteria. In particular, we find that the equilibrium constant for the metabolic networks decreases significantly in-line with variability in bacterial habitats, supporting the view that environmental variability promotes disequilibrium within these biochemical reaction system

Fermion family recurrences in the Dyson-Schwinger formalism

We study the multiple solutions of the truncated propagator Dyson-Schwinger equation for a simple fermion theory with Yukawa coupling to a scalar field. Upon increasing the coupling constant $g$, other parameters being fixed, more than one non-perturbative solution breaking chiral symmetry becomes possible and we find these numerically. These ``recurrences'' appear as a mechanism to generate different fermion generations as quanta of the same fundamental field in an interacting field theory, without assuming any composite structure. The number of recurrences or flavors is reduced to a question about the value of the Yukawa coupling, and has no special profound significance in the Standard Model. The resulting mass function can have one or more nodes and the measurement that potentially detects them can be thought of as a collider-based test of the virtual dispersion relation $E=\sqrt{p^2+M(p^2)^2}$ for the charged lepton member of each family. This requires three independent measurements of the charged lepton's energy, three-momentum and off-shellness. We illustrate how this can be achieved for the (more difficult) case of the tau lepton

Analytical approach to chiral symmetry breaking in Minkowsky space

The mass gap equation for spontaneous chiral symmetry breaking is studied directly in Minkowsky space. In hadronic physics, spontaneous chiral symmetry breaking is crucial to generate a constituent mass for the quarks, and to produce the Partially Conserved Axial Current theorems, including a small mass for the pion. Here a class of finite kernels is used, expanded in Yukawa interactions. The Schwinger-Dyson equation is solved with an analytical approach. This improves the state of the art of solving the mass gap equation, which is usually solved with the equal-time approximation or with the Euclidean approximation. The mapping from the Euclidean space to the Minkowsky space is also illustrated.Comment: 7 pages, 3 figure

Dynamic communicability predicts infectiousness

Using real, time-dependent social interaction data, we look at correlations between some recently proposed dynamic centrality measures and summaries from large-scale epidemic simulations. The evolving network arises from email exchanges. The centrality measures, which are relatively inexpensive to compute, assign rankings to individual nodes based on their ability to broadcast information over the dynamic topology. We compare these with node rankings based on infectiousness that arise when a full stochastic SI simulation is performed over the dynamic network. More precisely, we look at the proportion of the network that a node is able to infect over a fixed time period, and the length of time that it takes for a node to infect half the network.We find that the dynamic centrality measures are an excellent, and inexpensive, proxy for the full simulation-based measures

Lorentzian regularization and the problem of point-like particles in general relativity

The two purposes of the paper are (1) to present a regularization of the self-field of point-like particles, based on Hadamard's concept of ``partie finie'', that permits in principle to maintain the Lorentz covariance of a relativistic field theory, (2) to use this regularization for defining a model of stress-energy tensor that describes point-particles in post-Newtonian expansions (e.g. 3PN) of general relativity. We consider specifically the case of a system of two point-particles. We first perform a Lorentz transformation of the system's variables which carries one of the particles to its rest frame, next implement the Hadamard regularization within that frame, and finally come back to the original variables with the help of the inverse Lorentz transformation. The Lorentzian regularization is defined in this way up to any order in the relativistic parameter 1/c^2. Following a previous work of ours, we then construct the delta-pseudo-functions associated with this regularization. Using an action principle, we derive the stress-energy tensor, made of delta-pseudo-functions, of point-like particles. The equations of motion take the same form as the geodesic equations of test particles on a fixed background, but the role of the background is now played by the regularized metric.Comment: 34 pages, to appear in J. Math. Phy

Field theory description of vacuum replicas

In this paper we develop a systematic quantum field theory based approach to the vacuum replica recently found to exist in effective low energy models in hadronic physics. A local operator creating the replica state is constructed explicitly. We show that a new effective quark-quark force arises in result of replica existence. Phenomenological implications of such a force are also briefly discussed.Comment: RevTeX4, 23 pages, 4 Postscript figures, uses epsfig.sty, to appear in Phys.Rev.

Multitask Learning on Graph Neural Networks: Learning Multiple Graph Centrality Measures with a Unified Network

The application of deep learning to symbolic domains remains an active research endeavour. Graph neural networks (GNN), consisting of trained neural modules which can be arranged in different topologies at run time, are sound alternatives to tackle relational problems which lend themselves to graph representations. In this paper, we show that GNNs are capable of multitask learning, which can be naturally enforced by training the model to refine a single set of multidimensional embeddings $\in \mathbb{R}^d$ and decode them into multiple outputs by connecting MLPs at the end of the pipeline. We demonstrate the multitask learning capability of the model in the relevant relational problem of estimating network centrality measures, focusing primarily on producing rankings based on these measures, i.e. is vertex $v_1$ more central than vertex $v_2$ given centrality $c$?. We then show that a GNN can be trained to develop a \emph{lingua franca} of vertex embeddings from which all relevant information about any of the trained centrality measures can be decoded. The proposed model achieves $89\%$ accuracy on a test dataset of random instances with up to 128 vertices and is shown to generalise to larger problem sizes. The model is also shown to obtain reasonable accuracy on a dataset of real world instances with up to 4k vertices, vastly surpassing the sizes of the largest instances with which the model was trained ($n=128$). Finally, we believe that our contributions attest to the potential of GNNs in symbolic domains in general and in relational learning in particular.Comment: Published at ICANN2019. 10 pages, 3 Figure

A Systematic Search for High Surface Brightness Giant Arcs in a Sloan Digital Sky Survey Cluster Sample

We present the results of a search for gravitationally-lensed giant arcs conducted on a sample of 825 SDSS galaxy clusters. Both a visual inspection of the images and an automated search were performed and no arcs were found. This result is used to set an upper limit on the arc probability per cluster. We present selection functions for our survey, in the form of arc detection efficiency curves plotted as functions of arc parameters, both for the visual inspection and the automated search. The selection function is such that we are sensitive only to long, high surface brightness arcs with g-band surface brightness mu_g 10. Our upper limits on the arc probability are compatible with previous arc searches. Lastly, we report on a serendipitous discovery of a giant arc in the SDSS data, known inside the SDSS Collaboration as Hall's arc.Comment: 34 pages,8 Fig. Accepted ApJ:Jan-200

Effects of multiple abiotic stresses on lipids and sterols profile in barley leaves (Hordeum vulgare L.)

open6siPlants are usually exposed to several types of abiotic stress in regular field conditions. The lipid profile of barley homozygous lines exposed to drought, heat, salinity, and their combinations, was investigated in the present study. Free fatty acids, free sterols, and diacylglycerols were the most abundant classes (∼8.0% of plant material). The genetic background significantly impacted the lipid composition rather than the treatments, and diacylglycerols were the only lipid class affected by salinity (1.84 mg/100 mg plant tissue; ∼33% reduction). However, the genotype × treatment interaction analysis revealed that the lipid and sterol compositions depended on both genotype and environment. Our results suggest that inborn stress tolerance in barley is manifested by enhanced accumulation of most lipids, mainly sterols, especially in heat/drought-stressed plants. In addition, expression of the LTP2 gene may be indirectly involved in the abiotic stress reaction of barley by mediating intracellular transport of some lipid classesopenA. Kuczyńska; V. Cardenia; P. Ogrodowicza; .M. Kempa; M. T. Rodriguez-Estrada; K. MikołajczakaA. Kuczyńska; V. Cardenia; P. Ogrodowicza; .M. Kempa; M. T. Rodriguez-Estrada; K. Mikołajczak