On Vanishing Sums of Roots of Unity in Polynomial Calculus and Sum-Of-Squares

Vanishing sums of roots of unity can be seen as a natural generalization of knapsack from Boolean variables to variables taking values over the roots of unity. We show that these sums are hard to prove for polynomial calculus and for sum-of-squares, both in terms of degree and size

Abstract Canonical Inference

An abstract framework of canonical inference is used to explore how different proof orderings induce different variants of saturation and completeness. Notions like completion, paramodulation, saturation, redundancy elimination, and rewrite-system reduction are connected to proof orderings. Fairness of deductive mechanisms is defined in terms of proof orderings, distinguishing between (ordinary) "fairness," which yields completeness, and "uniform fairness," which yields saturation.Comment: 28 pages, no figures, to appear in ACM Trans. on Computational Logi

Matemática, informática y la “renegociación” de normas preexistentes

El deseo de dar respuestas a interrogantes tales como ¿Qué tipo de conocimientos requiere una sociedad en constante transformación?; ¿qué capacidades o estrategias debemos promover para favorecer la formación de individuos social, cultural e intelectualmente plenos, comprometidos con su entorno?. ¿Será posible contemplar en las planificaciones pedagógicas la secuencia evolutiva natural de la vida (ambiente enseñanzas- memorias-comportamiento individual-comportamiento social-enseñanzas-ambiente), los tiempos biológicos requeridos para consolidar, almacenar y dar funcionalidad a la información adquirida?; ¿imponerse a la aceleración (o inercia) de los tiempos administrativos? nos lleva a reflexionar sobre la propia práctica, considerar el rediseño de la misma, a proponernos finalmente un plan de trabajo cuya estructuración contemple tanto cuestiones atinentes a la propia disciplina como, y especialmente, a todas aquellas otras que tuvieran que ver con una positiva integración Sociedad, Ciencia y Tecnología, S/C/T. En una primer etapa procedimos a investigar, caracterizar y explicitar una serie de normas “sociomatemáticas” que llamamos preexistentes y que a nuestro juicio serían inhibidoras del aprendizaje y relativas al contexto sociocultural en el que nos movemos. Por contraposición establecimos normas a renegociar con nuestros estudiantes, las que llamamos “emergentes”. Concretada la primer etapa del plan (sistema de interpretación, diseño de instrumentos para la intervención pedagógica) generamos experiencias participativas con la presencia de estudiantes y docentes a los fines de implementar los instrumentos diseñados, observar y evaluar la calidad de los mismos, el sistema de interpretación en sí. El presente trabajo trata de algunos resultados y conclusiones obtenidas en esta segunda etapa del plan

Las funciones en la resolución de problemas

En este trabajo presentamos algunas reflexiones y una propuesta acerca de la enseñanza por resolución de problemas, siendo el eje de esta última la aplicación y discusión del concepto de Función. En las carreras ´no matemáticas´ sin relegar el papel fundamental de la formación en lo teórico-conceptual los esfuerzos se desplazan hacia la aplicación de los métodos matemáticos en la resolución de problemas de las ciencias en general. Dado que el desarrollo mismo de la ciencia puede entenderse como resultado de la búsqueda de solución a los distintos problemas que aquejan al hombre, creemos que la ´enseñanza por resolución de problemas´ coadyuva a promover el cambio conceptual y metodológico que requiere actualmente el sistema educativo en general. La propuesta consiste esencialmente en el planteo de una situación problemática familiar al estudiante para, a partir de allí y siempre bajo la guía y supervisión del docente, proceder a su discusión, al planteo de conjeturas e hipótesis, resolución, verificación, etc. En este caso el problema requiere del concepto de función, concepto básico y esencial en toda disciplina que acuda a los modelos matemáticos. Creemos que este presenta características que lo signan como concepto fuerza en la implementación del cambio pretendido; que su uso en el marco de la resolución de problemas coadyuva a tal propósito pues, entre otras bondades, las funciones se caracterizan por tener cuatro representaciones o codificaciones distintas -gráfica, numérica, analítica, verbal- cada una de las cuales expresa aspectos o propiedades didácticas no equivalentes ni equiparables entre sí, lo cual, además de ampliar el espectro de posibilidades para trabajar con el estudiante, proporciona elementos para una mejor evaluación del mismo (asimilando la comprensión del concepto a la capacidad de recodificar la información desde una representación a otra)

A novel implantation technique for engineered osteo-chondral grafts

We present a novel method to support precise insertion of engineered osteochondral grafts by pulling from the bone layer, thereby minimizing iatrogenic damage associated with direct manipulation of the cartilage layer. Grafts were generated by culturing human expanded chondrocytes on Hyaff®-11 meshes, sutured to Tutobone® spongiosa cylinders. Through the bone layer, shaped to imitate the surface-contours of the talar dome, two sutures were applied: the first for anterograde implantation, to pull the graft into the defect, and the second for retrograde correction, in case of a too deep insertion. All grafts could be correctly positioned into osteochondral lesions created in cadaveric ankle joints with good fit to the surrounding cartilage. Implants withstood short-term dynamic stability tests applied to the ankle joint, without delamination or macroscopic damage. The developed technique, by allowing precise and stable positioning of osteochondral grafts without iatrogenic cartilage damage, is essential for the implantation of engineered tissues, where the cartilage layer is not fully mechanically developed, and could be considered also for conventional autologous osteochondral transplantatio

Comparative chondrogenesis of human cells in a 3D integrated experimental/computational mechanobiology model

We present an integrated experimental–computational mechanobiology model of chondrogenesis. The response of human articular chondrocytes to culture medium perfusion, versus perfusion associated with cyclic pressurisation, versus non-perfused culture, was compared in a pellet culture model, and multiphysic computation was used to quantify oxygen transport and flow dynamics in the various culture conditions. At 2 weeks of culture, the measured cell metabolic activity and the matrix content in collagen type II and aggrecan were greatest in the perfused+ pressurised pellets. The main effects of perfusion alone, relative to static controls, were to suppress collagen type I and GAG contents, which were greatest in the non-perfused pellets. All pellets showed a peripheral layer of proliferating cells, which was thickest in the perfused pellets, and most pellets showed internal gradients in cell density and matrix composition. In perfused pellets, the computed lowest oxygen concentration was 0.075mM (7.5% tension), the maximal oxygen flux was 477.5 nmol/m2/s and the maximal fluid shear stress, acting on the pellet surface, was 1.8mPa (0.018 dyn/cm2). In the non-perfused pellets, the lowest oxygen concentration was 0.003mM (0.3% tension) and the maximal oxygen flux was 102.4nmol/m2/s.Alocal correlationwas observed, between the gradients in pellet properties obtained from histology, and the oxygen fields calculated with multiphysic simulation. Our results showup-regulation of hyalinematrix protein production by human chondrocytes in response to perfusion associated with cyclic pressurisation. These results could be favourably exploited in tissue engineering applications

Scavenger 0.1: A Theorem Prover Based on Conflict Resolution

This paper introduces Scavenger, the first theorem prover for pure first-order logic without equality based on the new conflict resolution calculus. Conflict resolution has a restricted resolution inference rule that resembles (a first-order generalization of) unit propagation as well as a rule for assuming decision literals and a rule for deriving new clauses by (a first-order generalization of) conflict-driven clause learning.Comment: Published at CADE 201

New results on rewrite-based satisfiability procedures

Program analysis and verification require decision procedures to reason on theories of data structures. Many problems can be reduced to the satisfiability of sets of ground literals in theory T. If a sound and complete inference system for first-order logic is guaranteed to terminate on T-satisfiability problems, any theorem-proving strategy with that system and a fair search plan is a T-satisfiability procedure. We prove termination of a rewrite-based first-order engine on the theories of records, integer offsets, integer offsets modulo and lists. We give a modularity theorem stating sufficient conditions for termination on a combinations of theories, given termination on each. The above theories, as well as others, satisfy these conditions. We introduce several sets of benchmarks on these theories and their combinations, including both parametric synthetic benchmarks to test scalability, and real-world problems to test performances on huge sets of literals. We compare the rewrite-based theorem prover E with the validity checkers CVC and CVC Lite. Contrary to the folklore that a general-purpose prover cannot compete with reasoners with built-in theories, the experiments are overall favorable to the theorem prover, showing that not only the rewriting approach is elegant and conceptually simple, but has important practical implications.Comment: To appear in the ACM Transactions on Computational Logic, 49 page