The Sizing and Optimization Language (SOL): A computer language to improve the user/optimizer interface

The nonlinear mathematical programming method (formal optimization) has had many applications in engineering design. A figure illustrates the use of optimization techniques in the design process. The design process begins with the design problem, such as the classic example of the two-bar truss designed for minimum weight as seen in the leftmost part of the figure. If formal optimization is to be applied, the design problem must be recast in the form of an optimization problem consisting of an objective function, design variables, and constraint function relations. The middle part of the figure shows the two-bar truss design posed as an optimization problem. The total truss weight is the objective function, the tube diameter and truss height are design variables, with stress and Euler buckling considered as constraint function relations. Lastly, the designer develops or obtains analysis software containing a mathematical model of the object being optimized, and then interfaces the analysis routine with existing optimization software such as CONMIN, ADS, or NPSOL. This final state of software development can be both tedious and error-prone. The Sizing and Optimization Language (SOL), a special-purpose computer language whose goal is to make the software implementation phase of optimum design easier and less error-prone, is presented

Limits on chemical complexity in diffuse clouds: search for CH3OH and HC5N absorption

Context: An unexpectedly complex polyatomic chemistry exists in diffuse clouds, allowing detection of species such as C2H, C3H2, H2CO and NH3 which have relative abundances that are strikingly similar to those inferred toward the dark cloud TMC-1 Aims: We probe the limits of complexity of diffuse cloud polyatomic chemistry. Methods: We used the IRAM Plateau de Bure Interferometer to search for galactic absorption from low-lying J=2-1 rotational transitions of A- and E-CH3OH near 96.740 GHz and used the VLA to search for the J=8-7 transition of HC5N at 21.3 GHz. Results: Neither CH3OH nor HC5N were detected at column densities well below those of all polyatomics known in diffuse clouds and somewhat below the levels expected from comparison with TMC-1. The HCN/HC5N ratio is at least 3-10 times higher in diffuse gas than toward TMC-1. Conclusions: It is possible to go to the well once (or more) too ofte

Targeted Recovery as an Effective Strategy against Epidemic Spreading

We propose a targeted intervention protocol where recovery is restricted to individuals that have the least number of infected neighbours. Our recovery strategy is highly efficient on any kind of network, since epidemic outbreaks are minimal when compared to the baseline scenario of spontaneous recovery. In the case of spatially embedded networks, we find that an epidemic stays strongly spatially confined with a characteristic length scale undergoing a random walk. We demonstrate numerically and analytically that this dynamics leads to an epidemic spot with a flat surface structure and a radius that grows linearly with the spreading rate.Comment: 6 pages, 5 figure

Clustering of spectra and fractals of regular graphs

We exhibit a characteristic structure of the class of all regular graphs of degree d that stems from the spectra of their adjacency matrices. The structure has a fractal threadlike appearance. Points with coordinates given by the mean and variance of the exponentials of graph eigenvalues cluster around a line segment that we call a filar. Zooming-in reveals that this cluster splits into smaller segments (filars) labeled by the number of triangles in graphs. Further zooming-in shows that the smaller filars split into subfilars labelled by the number of quadrangles in graphs, etc. We call this fractal structure, discovered in a numerical experiment, a multifilar structure. We also provide a mathematical explanation of this phenomenon based on the Ihara-Selberg trace formula, and compute the coordinates and slopes of all filars in terms of Bessel functions of the first kind.Comment: 10 pages, 5 figure

Consistent Gravitationally-Coupled Spin-2 Field Theory

Inspired by the translational gauge structure of teleparallel gravity, the theory for a fundamental massless spin-2 field is constructed. Accordingly, instead of being represented by a symmetric second-rank tensor, the fundamental spin-2 field is assumed to be represented by a spacetime (world) vector field assuming values in the Lie algebra of the translation group. The flat-space theory naturally emerges in the Fierz formalism and is found to be equivalent to the usual metric-based theory. However, the gravitationally coupled theory, with gravitation itself described by teleparallel gravity, is shown not to present the consistency problems of the spin-2 theory constructed on the basis of general relativity.Comment: 16 pages, no figures. V2: Presentation changes, including addition of a new sub-section, aiming at clarifying the text; version accepted for publication in Class. Quantum Grav

Generation of bipartite spin entanglement via spin-independent scattering

We consider the bipartite spin entanglement between two identical fermions generated in spin-independent scattering. We show how the spatial degrees of freedom act as ancillas for the creation of entanglement to a degree that depends on the scattering angle, $\theta$. The number of Slater determinants generated in the process is greater than 1, corresponding to genuine quantum correlations between the identical fermions. The maximal entanglement attainable of 1 ebit is reached at $\theta=\pi/2$. We also analyze a simple $\theta$ dependent Bell's inequality, which is violated for $\pi/4<\theta\leq\pi/2$. This phenomenon is unrelated to the symmetrization postulate but does not appear for unequal particles.Comment: 5 pages and 3 figures. Accepted in PR

Use of Logical Models for Proving Operational Termination in General Logics

The final publication is available at Springer via http://dx.doi.org/10.1007/978-3-319-44802-2_2[EN] A declarative programming language is based on some logic L and its operational semantics is given by a proof calculus which is often presented in a natural deduction style by means of inference rules. Declarative programs are theories S of L and executing a program is proving goals &#981; in the inference system I(S) associated to S as a particulariza-tion of the inference system of the logic. The usual soundness assumption for L implies that every model A of S also satisfies &#981;. In this setting, the operational termination of a declarative program is quite naturally defined as the absence of infinite proof trees in the inference system I(S). Proving operational termination of declarative programs often involves two main ingredients: (i) the generation of logical models A to abstract the program execution (i.e., the provability of specific goals in I(S)), and (ii) the use of well-founded relations to guarantee the absence of infinite branches in proof trees and hence of infinite proof trees, possibly taking into account the information about provability encoded by A. In this paper we show how to deal with (i) and (ii) in a uniform way. The main point is the synthesis of logical models where well-foundedness is a side requirement for some specific predicate symbols.Partially supported by the EU (FEDER), Spanish MINECO TIN 2013-45732-C4-1-P and TIN2015-69175-C4-1-R, and GV PROMETEOII/2015/013.Lucas Alba, S. (2016). Use of Logical Models for Proving Operational Termination in General Logics. Lecture Notes in Computer Science. 9942:26-46. https://doi.org/10.1007/978-3-319-44802-2S2646994