Causal Theory for the Gauged Thirring Model

We consider the (2+1)-dimensional massive Thirring model as a gauge theory, with one fermion flavor, in the framework of the causal perturbation theory and address the problem of dynamical mass generation for the gauge boson. In this context we get an unambiguous expression for the coefficient of the induced Chern-Simons term.Comment: LaTex, 21 pages, no figure

Axial Anomaly through Analytic Regularization

In this work we consider the 2-point Green's functions in (1+1) dimensional quantum electrodynamics and show that the correct implementation of analytic regularization gives a gauge invariant result for the vaccum polarization amplitude and the correct coefficient for the axial anomaly.Comment: 8 pages, LaTeX, no figure

Radiative Corrections for the Gauged Thirring Model in Causal Perturbation Theory

We evaluate the one-loop fermion self-energy for the gauged Thirring model in (2+1) dimensions, with one massive fermion flavor, in the framework of the causal perturbation theory. In contrast to QED$_3$, the corresponding two-point function turns out to be infrared finite on the mass shell. Then, by means of a Ward identity, we derive the on-shell vertex correction and discuss the role played by causality for nonrenormalizable theories.Comment: LaTex, 09 pages, no figures. Title changed and introduction enlarged. To be published in Eur. Phys. J.

Gauged Thirring Model in the Heisenberg Picture

We consider the (2+1)-dimensional gauged Thirring model in the Heisenberg picture. In this context we evaluate the vacuum polarization tensor as well as the corrected gauge boson propagator and address the issues of generation of mass and dynamics for the gauge boson (in the limits of QED$_3$ and Thirring model as a gauge theory, respectively) due to the radiative corrections.Comment: 14 pages, LaTex, no figure

Runtime analysis of mutation-based geometric semantic genetic programming on boolean functions.

Geometric Semantic Genetic Programming (GSGP) is a recently introduced form of Genetic Programming (GP), rooted in a geometric theory of representations, that searches directly the semantic space of functions/programs, rather than the space of their syntactic representations (e.g., trees) as in traditional GP. Remarkably, the fitness landscape seen by GSGP is always – for any domain and for any problem – unimodal with a linear slope by construction. This has two important consequences: (i) it makes the search for the optimum much easier than for traditional GP; (ii) it opens the way to analyse theoretically in a easy manner the optimisation time of GSGP in a general setting. The runtime analysis of GP has been very hard to tackle, and only simplified forms of GP on specific, unrealistic problems have been studied so far. We present a runtime analysis of GSGP with various types of mutations on the class of all Boolean functionsThe authors are grateful to Dirk Sudholt for helping check the proofs. Alberto Moraglio was supported by EPSRC grant EP/I010297/

Commentary on “Jaws 30”, by W. B. Langdon

While genetic programming has had a huge impact on the research community, it is fair to say that its impact on industry and practitioners has been much smaller. In this commentary we elaborate on this claim and suggest some broad research goals aimed at greatly increasing such impact

Heuristic search of (semi-)bent functions based on cellular automata

An interesting thread in the research of Boolean functions for cryptography and coding theory is the study of secondary constructions: given a known function with a good cryptographic profile, the aim is to extend it to a (usually larger) function possessing analogous properties. In this work, we continue the investigation of a secondary construction based on cellular automata (CA), focusing on the classes of bent and semi-bent functions. We prove that our construction preserves the algebraic degree of the local rule, and we narrow our attention to the subclass of quadratic functions, performing several experiments based on exhaustive combinatorial search and heuristic optimization through Evolutionary Strategies (ES). Finally, we classify the obtained results up to permutation equivalence, remarking that the number of equivalence classes that our CA-XOR construction can successfully extend grows very quickly with respect to the CA diameter

Evaluating space measures in P systems

P systems with active membranes are a variant of P systems where membranes can be created by division of existing membranes, thus creating an exponential amount of resources in a polynomial number of steps. Time and space complexity classes for active membrane systems have been introduced, to characterize classes of problems that can be solved by different membrane systems making use of different resources. In particular, space complexity classes introduced initially considered a hypothetical real implementation by means of biochemical materials, assuming that every single object or membrane requires some constant physical space (corresponding to unary notation). A different approach considered implementation of P systems in silico, allowing to store the multiplicity of each object in each membrane using binary numbers. In both cases, the elements contributing to the definition of the space required by a system (namely, the total number of membranes, the total number of objects, the types of different membranes, and the types of different objects) was considered as a whole. In this paper, we consider a different definition for space complexity classes in the framework of P systems, where each of the previous elements is considered independently. We review the principal results related to the solution of different computationally hard problems presented in the literature, highlighting the requirement of every single resource in each solution. A discussion concerning possible alternative solutions requiring different resources is presented

Probabilistic reconstruction via machine-learning of the Po watershed aquifer system (Italy)

A machine-learning-based methodology is proposed to delineate the spatial distribution of geomaterials across a large-scale three-dimensional subsurface system. The study area spans the entire Po River Basin in northern Italy. As uncertainty quantification is critical for subsurface characterization, the methodology is specifically designed to provide a quantitative evaluation of prediction uncertainty at each location of the reconstructed domain. The analysis is grounded on a unique dataset that encompasses lithostratigraphic data obtained from diverse sources of information. A hyperparameter selection technique based on a stratified cross-validation procedure is employed to improve model prediction performance. The quality of the results is assessed through validation against pointwise information and available hydrogeological cross-sections. The large-scale patterns identified are in line with the main features highlighted by typical hydrogeological surveys. Reconstruction of prediction uncertainty is consistent with the spatial distribution of available data and model accuracy estimates. It enables one to identify regions where availability of new information could assist in the constraining of uncertainty. The comprehensive dataset provided in this study, complemented by the model-based reconstruction of the subsurface system and the assessment of the associated uncertainty, is relevant from a water resources management and protection perspective. As such, it can be readily employed in the context of groundwater availability and quality studies aimed at identifying the main dynamics and patterns associated with the action of climate drivers in large-scale aquifer systems of the kind here analyzed, while fully embedding model and parametric uncertainties that are tied to the scale of investigation