The degree-distance and transmission-adjacency matrices

Let $G$ be a connected graph with adjacency matrix $A(G)$. The distance matrix $D(G)$ of $G$ has rows and columns indexed by $V(G)$ with $uv$-entry equal to the distance $\mathrm{dist}(u,v)$ which is the number of edges in a shortest path between the vertices $u$ and $v$. The transmission $\mathrm{trs}(u)$ of $u$ is defined as $\sum_{v\in V(G)}\mathrm{dist}(u,v)$. Let $\mathrm{trs}(G)$ be the diagonal matrix with the transmissions of the vertices of $G$ in the diagonal, and $\mathrm{deg}(G)$ the diagonal matrix with the degrees of the vertices in the diagonal. In this paper we investigate the Smith normal form (SNF) and the spectrum of the matrices $D^{\mathrm{deg}}_+(G):=\mathrm{deg}(G)+D(G)$, $D^{\mathrm{deg}}(G):=\mathrm{deg}(G)-D(G)$, $A^{\mathrm{trs}}_+(G):=\mathrm{trs}(G)+A(G)$ and $A^{\mathrm{trs}}(G):=\mathrm{trs}(G)-A(G)$. In particular, we explore how good the spectrum and the SNF of these matrices are for determining graphs up to isomorphism. We found that the SNF of $A^{\mathrm{trs}}$ has an interesting behaviour when compared with other classical matrices. We note that the SNF of $A^{\mathrm{trs}}$ can be used to compute the structure of the sandpile group of certain graphs. We compute the SNF of $D^{\mathrm{deg}}_+$, $D^{\mathrm{deg}}$, $A^{\mathrm{trs}}_+$ and $A^{\mathrm{trs}}$ for several graph families. We prove that complete graphs are determined by the SNF of $D^{\mathrm{deg}}_+$, $D^{\mathrm{deg}}$, $A^{\mathrm{trs}}_+$ and $A^{\mathrm{trs}}$. Finally, we derive some results about the spectrum of $D^{\mathrm{deg}}$ and $A^{\mathrm{trs}}$.Comment: 19 page

Descriptive complexity of controllable graphs

Let $G$ be a graph on $n$ vertices with adjacency matrix $A$, and let $\mathbf{1}$ be the all-ones vector. We call $G$ controllable if the set of vectors $\mathbf{1}, A\mathbf{1}, \dots, A^{n-1}\mathbf{1}$ spans the whole space $\mathbb{R}^n$. We characterize the isomorphism problem of controllable graphs in terms of other combinatorial, geometric and logical problems. We also describe a polynomial time algorithm for graph isomorphism that works for almost all graphs.Comment: 14 page

Descriptive complexity of controllable graphs

Let G be a graph on n vertices with adjacency matrix A, and let 1 be the all-ones vector. We call G controllable if the set of vectors 1, A1,., An-11 spans the whole space Rn. We characterize the isomorphism problem of controllable graphs in terms of other combinatorial, geometric and logical problems. We also describe a polynomial time algorithm for graph isomorphism that works for almost all graphs.</p

Descriptive complexity of graph spectra.

Two graphs are cospectral if their respective adjacency matrices have the same multi-set of eigenvalues. A graph is said to be determined by its spectrum if all graphs that are cospectral with it are isomorphic to it. We consider these properties in relation to logical definability. We show that any pair of graphs that are elementarily equivalent with respect to the three-variable counting first-order logic are cospectral, and this is not the case with , nor with any number of variables if we exclude counting quantifiers. We also show that the class of graphs that are determined by their spectra is definable in partial fixed-point logic with counting. We relate these properties to other algebraic and combinatorial problems.OZ was supported by CONACyT-Mexico Grant 384665, SS was supported by EPSRC and The Royal Society

Estudio de factibilidad para le mejoramiento del Micromercado "San Pedrito", ubicado en la Parroquia San Pedro de Taboada

El presente estudio desarrolla las estrategias orientadas al reposicionamiento de la empresa Micromercado San Pedrito ubicada en el la zona del Valle de la ciudad de Sangolquí; a través del rediseño de las estrategias de mercado y la investigación sobre las percepciones del cliente actual y potencial de la empresa, se desarrolló una nueva imagen para la organización, acorde a los servicios que esta presta y se incrementó una nueva línea de productos, puesto que la investigación de mercado reveló que en la zona de influencia del proyecto, esta línea de productos no está bien cubierta por la competencia existente y la implementación en el micromercado significaría darle una ventaja competitiva a la organización, además, el rediseño de la imagen de la empresa junto a la filosofía empresarial, contribuye a potenciar la capacidad de impacto en el mercado meta, aumentar los volúmenes de venta de la empresa e impulsar los productos cuyas ventas son sensiblemente más bajas; por ello se determinó que la organización genera ingresos con factibilidad económica a mediano plazo, lo que justifica las inversiones a realizar y provee plazas de trabajo adicionales.The current research develops strategies oriented to reposes San Pedro Market company located in the Valley zone of Sangolquí, among their clients; trough the design of market strategies and research over potential and actual client`s perceptions, it was developed a new company’s image according to the services that San Pedro market gives to its target market; it was increased a line of new products, which are composed by meat and other kind of the same kind; these new product were sold by packing in vacuum presentation and in a weight mode; it was developed this alternative, because the market research showed that the competitors do not cover these line of products, so the organization can get a significant advantage among target market; besides the redesign of the company’s image and philosophy will increased the sales amount of products whose income it significantly lower than star products; working in this way, it was determined that the organization will generate income enough to justified the investments required to achieve the goals of the company through economic feasibility

Logical Aspects of Probability and Quantum Computation

Most of the work presented in this document can be read as a sequel to previous work of the author and collaborators, which has been published and appears in [DSZ16, DSZ17, ABdSZ17]. In [ABdSZ17], the mathematical description of quantum homomorphisms of graphs and more generally of relational structures, using the language of category theory is given. In particular, we introduced the concept of ‘quantum’ monad. In this thesis we show that the quantum monad fits nicely into the categorical framework of effectus theory, developed by Jacobs et al. [Jac15, CJWW15]. Effectus theory is an emergent field in categorical logic aiming to describe logic and probability, from the point of view of classical and quantum computation. The main contribution in the first part of this document prove that the Kleisli category of the quantum monad on relational structures is an effectus. The second part is rather different. There, distinct facets of the equivalence relation on graphs called cospectrality are described: algebraic, combinatorial and logical relations are presented as sufficient conditions on graphs for having the same spectrum (i.e. being ‘cospectral’). Other equivalence of graphs (called fractional isomorphism) is also related using some ‘game’ comonads from Abramsky et al. [ADW17, Sha17, AS18]. We also describe a sufficient condition for a pair of graphs to be cospectral using the quantum monad: two Kleisli morphisms (going in opposite directions) between them satisfying certain compatibility requirement

The Quantum Monad on Relational Structures

Homomorphisms between relational structures play a central role in finite model theory, constraint satisfaction, and database theory. A central theme in quantum computation is to show how quantum resources can be used to gain advantage in information processing tasks. In particular, non-local games have been used to exhibit quantum advantage in boolean constraint satisfaction, and to obtain quantum versions of graph invariants such as the chromatic number. We show how quantum strategies for homomorphism games between relational structures can be viewed as Kleisli morphisms for a quantum monad on the (classical) category of relational structures and homomorphisms. We use these results to exhibit a wide range of examples of contextuality-powered quantum advantage, and to unify several apparently diverse strands of previous work

Compressive strength of partially stiffened cylinders at elevated temperatures

Este trabajo presenta el análisis de elementos finitos de cilindros parcialmente rígidos sometidos a compresión axial a temperaturas elevadas. La resistencia a la compresión se calcula para las condiciones de peso propio y también se investiga la influencia de la temperatura en la respuesta del material. En la industria del petróleo, los recipientes a presión se utilizan comúnmente para operar en condiciones de diseño complejas, como perfiles de alta presión y/o gradientes de temperatura elevados que afectan considerablemente la respuesta estructural de los componentes internos. Entre ellos, los raisers se convierten en elementos de acero sensibles que soportan una carga alta de compresión debido al peso propio, así como, elementos de aislamiento agregados para protegerlos del gradiente de temperatura elevada. La mayoría de los raisers fallan estructuralmente en el extremo inferior debido a la deformación causada por el peso propio y los efectos de temperatura. Para remediar esta situación y garantizar la integridad de la tubería vertical, los refuerzos longitudinales están soldados en el extremo inferior. Por lo tanto, se requiere una evaluación adecuada de la resistencia a la compresión del cilindro, teniendo en cuenta la influencia del refuerzo&nbsp;longitudinal y la temperatura correspondiente. Los resultados indican que el uso de refuerzos longitudinales en cilindros deformados aumenta la resistencia al pandeo en porcentajes que varían de acuerdo con la sección transversal de los perfiles.This work presents the finite element analysis of partially stiffened cylinders subjected to axial compression at elevated temperatures. The compressive strength is calculated for self-weight conditions and the influence of the temperature on the material response is also investigated. In the oil industry, pressure vessels are commonly used operating at complex design conditions such as high-pressure profiles and/or elevated temperature gradients which affect considerably the structural response of inner components. Among them, risers become sensitive steel elements withstanding heavy compressive loading due to self-weight, as well as, insulation elements added to protect them from the elevated temperature gradient. Most risers structurally fail at the bottom end due to buckling caused by self-weight and temperature effects. To remediate this situation and to guarantee the integrity of the riser, longitudinal stiffeners are welded at the bottom end. Hence, a proper determination of the compressive strength of the cylinder, taking into account the influence of the longitudinal stiffening and the corresponding temperature, is required. Results indicate that the use of longitudinal stiffeners in deformed cylinders increases the strength to buckling in percentages that vary according to the cross-section of the profiles. &nbsp

Análisis del contenido y la capacidad antioxidante y de la aceptación de la bebida de café mediante métodos de preparación con filtración por gravedad

Most gravity-filtration coffee preparation methods constitute good alternatives for obtaining coffee with varying acidity, bitterness, and bodies. The present study identifies the composition of compounds with antioxidant capacities and cup profiles for coffee beverages prepared using eight gravity-filtration methods. UV-visible spectrophotometry and high-performance liquid chromatography  quantified antioxidants, hydroxycinnamic acids, and antioxidant activity. A qualitative descriptive analysis was performed using an expert panel to establish the sensory quality. The methods that yielded the highest total phenol and flavonoid concentrations were Chemex, Siphon, and Silvertone. The Silvertone, Siphon, and Neapolitan methods had the most condensed tannin content. The maximum hydroxycinnamic acid content was found with the Siphon and Neapolitan methods. Antioxidant capacity was evaluated by the ABTS (antioxidant capacity of the cationic radical 2,2-Azino-bis-3-ethylbenzthiazoline-6-sulfonic acid), ORAC (Oxygen Radical Absorption Capacity), and FRAP (Ferric Reducing Antioxidant Power) methods and found to be the highest with the Silvertone, Siphon, and Neapolitan methods. The preparation methods with the highest sensorial scores were Silvertone and Chemex, while the lowest sensorial acceptance level was found with the Cloth filter method. Beverages made with the Kalita and Drip methods showed the lowest antioxidant compound expressions. The most predominant hydroxycinnamic acid was chlorogenic acid in the eight preparations studied. We thus recommend that coffee be consumed following preparation with the Silvertone, Siphon, or Neapolitan methods to increase antioxidant consumption in the diet. Should the consumer prefer bitter notes, these may be found with the Silvertone preparation method; otherwise, one may enjoy acidic notes in coffee beverages with the Siphon and Neapolitan methods.Los métodos de preparación de café de filtración por gravedad en su mayoría constituyen una buena alternativa para obtener café con diferentes notas de acidez, amargo y cuerpo. En este estudio, se determinó la composición de los compuestos con capacidad antioxidante y el perfil de taza en bebidas de café preparadas con ocho métodos de filtración por gravedad. Se aplicó espectrofotometría UV-visible y cromatografía líquida de alta eficiencia para cuantificar antioxidantes, ácidos hidroxicinámicos y la actividad antioxidante. Para establecer la calidad sensorial se aplicó el análisis descriptivo cualitativo mediante un panel de expertos. Los métodos con mayor concentración de fenoles totales y flavonoides fueron Chemex, Sifón y Silvertone. Los de mayor contenido de taninos condensados fueron Silvertone, Sifón y Napolitana. El mayor contenido de ácidos hidroxicinámicos lo presentaron los métodos Sifón y Napolitana. La capacidad antioxidante se evaluó mediante los métodos ABTS (capacidad antioxidante del radical catiónico 2,2-Azino-bis-3-etilbenzotiazolin-6-sulfónico), ORAC (Capacidad de Absorción de Radicales de Oxígeno), and FRAP (Poder Antioxidante Reductor del Hierro) y fue alta en Silvertone, Sifón y Napolitana. Las preparaciones con mayor calificación sensorial fueron Silvertone y Chemex. El método con menor aceptación a nivel sensorial fue el método que empleó el colador de Tela. Las bebidas preparadas mediante Kalita y Goteo obtuvieron la más baja expresión de sus compuestos antioxidantes. El ácido hidroxicinámico más predominante en las ocho preparaciones estudiadas fue el ácido clorogénico. Se recomienda el consumo de café con los métodos Silvertone, Sifón y Napolitana para aumentar el consumo de antioxidantes en la dieta. Si el consumidor prefiere notas amargas, con Silvertone las encuentra; de lo contrario, con el método Sifón y Napolitana puede disfrutar de notas ácidas en la bebida de café