A dynamical metric and its ground state from the breaking down of the topological invariance of the Euler characteristic

Quantum state wave functionals are constructed in exact form for the graviton-like field theory obtained by breaking down the topological symmetry of the string action related with the Euler characteristic of the world-surface; their continuous and discrete symmetries are discussed. The comparison with the so-called Chern-Simons state, which may be inappropriate as quantum state, allows us to conclude that the found wave functionals will give a plausible approximation to the ground state for the considered field theory

Minimally non-local nucleon-nucleon potentials with chiral two-pion exchange including Δ\Delta's

We construct a coordinate-space chiral potential, including $\Delta$-isobar intermediate states in its two-pion-exchange component. The contact interactions entering at next-to-leading and next-to-next-to-next-to-leading orders ($Q^2$ and $Q^4$, respectively, $Q$ denoting generically the low momentum scale) are rearranged by Fierz transformations to yield terms at most quadratic in the relative momentum operator of the two nucleons. The low-energy constants multiplying these contact interactions are fitted to the 2013 Granada database, consisting of 2309 $pp$ and 2982 $np$ data (including, respectively, 148 and 218 normalizations) in the laboratory-energy range 0--300 MeV. For the total 5291 $pp$ and $np$ data in this range, we obtain a $\chi^2$/datum of roughly 1.3 for a set of three models characterized by long- and short-range cutoffs, $R_{\rm L}$ and $R_{\rm S}$ respectively, ranging from $(R_{\rm L},R_{\rm S})=(1.2,0.8)$ fm down to $(0.8,0.6)$ fm. The long-range (short-range) cutoff regularizes the one- and two-pion exchange (contact) part of the potential.Comment: 32 pages, 19 figures, accepted for publication as a Regular Article in Physical Review

Phenomenological High Precision Neutron-Proton Delta-Shell Potential

We provide a successful fit for proton-neutron scattering below pion production threshold up to LAB energies of 350 MeV. We use seven high-quality fits based on potentials with different forms as a measure of the systematic uncertainty. We represent the interaction as a sum of delta-shells in configuration space below the 3fm and a charge dependent one pion exchange potential above 3fm together with magnetic and vacuum polarization effects. Special attention is paid to estimate the errors of the phenomenological interaction.Comment: 5 pages, 2 figures. Comments and one figure with differential observables adde

Orthogonal basis with a conicoid first mode for shape specification of optical surfaces: Reply

We present some comments to the paper “Orthogonal basis with a conicoid first mode for shape specification of optical surfaces: comment.

Deciding Entailments in Inductive Separation Logic with Tree Automata

Separation Logic (SL) with inductive definitions is a natural formalism for specifying complex recursive data structures, used in compositional verification of programs manipulating such structures. The key ingredient of any automated verification procedure based on SL is the decidability of the entailment problem. In this work, we reduce the entailment problem for a non-trivial subset of SL describing trees (and beyond) to the language inclusion of tree automata (TA). Our reduction provides tight complexity bounds for the problem and shows that entailment in our fragment is EXPTIME-complete. For practical purposes, we leverage from recent advances in automata theory, such as inclusion checking for non-deterministic TA avoiding explicit determinization. We implemented our method and present promising preliminary experimental results

Dialectical Interrelation Between: Problematic Situation, Real Problem, Scientific Problem, Object and Field, in the Investigation Design: A Necessary Reflection

All research responds to the need of solutions to a problem that directly or indirectly affects society. The development of the same largely certifies and determines the constant search for solutions. The main objective of the present study was to arrive at a clear conceptualization, as complete as possible, of some the most important terms that come up during an investigation design: Problematic Situation, Real Problem, Scientific Problem, and Object and Field, given the visible shortcomings observed in pre- and post-graduate theses when the research work is being developed and defended. The methodology consisted of basically developing a reflection around these terms (the vision that different authors have in this regard was very helpful), as well as the presentation of varied examples contributed to see the meaning of these important concepts more clearly. The study shows in a scientifically grounded way the achievement of the above. The way in which the presentation of the different concepts was handled removes any possibility of mistakes. Keywords: methodology scientific investigation, problem, object, field. Resumen Toda investigación parte del apremio en dar una respuesta a la solución de un problema que afecta de una manera directa o indirecta a la Sociedad. En gran medida, el propio desarrollo de la misma compulsa y determina esa constante búsqueda de soluciones. El objetivo principal del presente estudio fue llegar a una conceptualización clara, y lo más acabada posible, de algunos de los más importantes términos que se manejan durante el diseño de una investigación: Situación Problémica, Problema Real, Problema Científico, Objeto y Campo, dada las visibles falencias que se observan en tesistas de pre y postgrado a la hora de desarrollar y defender sus trabajos de investigación. La metodología consistió, básicamente, en desarrollar una reflexión en torno a estos términos; para lo cual resultó de gran ayuda la visión que tienen diferentes autores al respecto; así como, la exposición de variados ejemplos contribuyó a ver más definidamente el significado de estos importantes conceptos. El estudio muestra de forma científicamente fundamentada el logro de lo anterior. La forma en que se maneja la presentación de los diferentes conceptos aleja toda posibilidad de equívocos. Palabras clave: metodología investigación científica, problema, objeto, campo

Spatial Interpolants

We propose Splinter, a new technique for proving properties of heap-manipulating programs that marries (1) a new separation logic-based analysis for heap reasoning with (2) an interpolation-based technique for refining heap-shape invariants with data invariants. Splinter is property directed, precise, and produces counterexample traces when a property does not hold. Using the novel notion of spatial interpolants modulo theories, Splinter can infer complex invariants over general recursive predicates, e.g., of the form all elements in a linked list are even or a binary tree is sorted. Furthermore, we treat interpolation as a black box, which gives us the freedom to encode data manipulation in any suitable theory for a given program (e.g., bit vectors, arrays, or linear arithmetic), so that our technique immediately benefits from any future advances in SMT solving and interpolation.Comment: Short version published in ESOP 201

Minimally Nonlocal Nucleon-Nucleon Potentials With Chiral Two-Pion Exchange Including Δ Resonances

We construct a coordinate-space chiral potential, including Δ -isobar intermediate states in its two-pion-exchange component up to order Q3 (Q denotes generically the low momentum scale). The contact interactions entering at next-to-leading and next-to-next-to-next-to-leading orders (Q2 and Q4 , respectively) are rearranged by Fierz transformations to yield terms at most quadratic in the relative momentum operator of the two nucleons. The low-energy constants multiplying these contact interactions are fitted to the 2013 Granada database, consisting of 2309 pp and 2982 np data (including, respectively, 148 and 218 normalizations) in the laboratory-energy range 0–300 MeV. For the total 5291 pp and np data in this range, we obtain a χ2 /datum of roughly 1.3 for a set of three models characterized by long- and short-range cutoffs, RL and RS , respectively, ranging from (RL ,RS)=(1.2, 0.8) fm down to (0.8,0.6) fm. The long-range (short-range) cutoff regularizes the one- and two-pion exchange (contact) part of the potential