Locally minimal uniformly oriented shortest networks

AbstractThe Steiner problem in a λ-plane is the problem of constructing a minimum length network interconnecting a given set of nodes (called terminals), with the constraint that all line segments in the network have slopes chosen from λ uniform orientations in the plane. This network is referred to as a minimum λ-tree. The problem is a generalization of the classical Euclidean and rectilinear Steiner tree problems, with important applications to VLSI wiring design.A λ-tree is said to be locally minimal if its length cannot be reduced by small perturbations of its Steiner points. In this paper we prove that a λ-tree is locally minimal if and only if the length of each path in the tree cannot be reduced under a special parallel perturbation on paths known as a shift. This proves a conjecture on necessary and sufficient conditions for locally minimal λ-trees raised in [M. Brazil, D.A. Thomas, J.F. Weng, Forbidden subpaths for Steiner minimum networks in uniform orientation metrics, Networks 39 (2002) 186–222]. For any path P in a λ-tree T, we then find a simple condition, based on the sum of all angles on one side of P, to determine whether a shift on P reduces, preserves, or increases the length of T. This result improves on our previous forbidden paths results in [M. Brazil, D.A. Thomas, J.F. Weng, Forbidden subpaths for Steiner minimum networks in uniform orientation metrics, Networks 39 (2002) 186–222]

Latitude does not influence cavity entrance orientation of South American avian excavators

In the Northern Hemisphere, several avian cavity excavators (e.g., woodpeckers) orient their cavities increasingly toward the equator as latitude increases (i.e., farther north), and it is proposed that they do so to take advantage of incident solar radiation at their nests. If latitude is a key driver of cavity orientations globally, this pattern should extend to the Southern Hemisphere. Here, we test the prediction that cavities are oriented increasingly northward at higher (i.e., colder) latitudes in the Southern Hemisphere and describe the preferred entrance direction(s) of 1501 cavities excavated by 25 avian species (n = 22 Picidae, 2 Trogonidae, 1 Furnariidae) across 12 terrestrial ecoregions (15°S ? 55°S) in South America. We used Bayesian projected normal mixed-effects models for circular data to examine the influence of latitude, and potential confounding factors, on cavity orientation. Also, a probability model selection procedure was used to simultaneously examine multiple orientation hypotheses in each ecoregion, to explore underlying cavity-orientation patterns. Contrary to predictions, and patterns from the Northern Hemisphere, birds did not orient their cavities more toward the equator with increasing latitude, suggesting that latitude may not be an important underlying selective force shaping excavation behavior in South America. Moreover, unimodal cavity-entrance orientations were not frequent among the ecoregions analyzed (infour ecoregions), whereas bimodal (in five ecoregions) or uniform (in three ecoregions) werealso common, although many of these patterns were not very sharp. Our results highlight the need to include data from under-studied biotas and regions to improve inferences at macroecology scales. Furthermore, we suggest a re-analysis of Northern Hemisphere cavity orientation patterns using a multimodel approach, and a more comprehensive assessment of the role of environmental factors as drivers of cavity orientation at different spatial scales in both hemispheres.Fil: Ojeda, Valeria Susana. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Patagonia Norte. Instituto de Investigaciones en Biodiversidad y Medioambiente. Universidad Nacional del Comahue. Centro Regional Universidad Bariloche. Instituto de Investigaciones en Biodiversidad y Medioambiente; ArgentinaFil: Schaaf, Alejandro Alberto. Universidad Nacional de Jujuy. Instituto de Ecorregiones Andinas. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Salta. Instituto de Ecorregiones Andinas; ArgentinaFil: Altamirano, Tatiana Edith. University of British Columbia; CanadáFil: Bonaparte, Eugenia Bianca. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Nordeste. Instituto de Biología Subtropical. Instituto de Biología Subtropical - Nodo Posadas | Universidad Nacional de Misiones. Instituto de Biología Subtropical. Instituto de Biología Subtropical - Nodo Posadas; ArgentinaFil: Bragagnolo, Laura Araceli. Universidad Nacional de La Pampa. Facultad de Ciencias Exactas y Naturales; ArgentinaFil: Chazarreta, L.. Secretaría de Ambiente y Desarrallo Sustentable de la Nación; ArgentinaFil: Cockle, Kristina Louise. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Nordeste. Instituto de Biología Subtropical. Instituto de Biología Subtropical - Nodo Posadas | Universidad Nacional de Misiones. Instituto de Biología Subtropical. Instituto de Biología Subtropical - Nodo Posadas; ArgentinaFil: Dias, R.. Universidade do Brasília; BrasilFil: Di Sallo, Facundo Gabriel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Nordeste. Instituto de Biología Subtropical. Instituto de Biología Subtropical - Nodo Posadas | Universidad Nacional de Misiones. Instituto de Biología Subtropical. Instituto de Biología Subtropical - Nodo Posadas; ArgentinaFil: Ibarra, T.. Pontificia Universidad Católica de Chile; ChileFil: Ippi, Silvina Graciela. Universidad Nacional del Comahue. Centro Regional Universitario Bariloche; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Jauregui, Adrian. Universidad Nacional de La Plata. Facultad de Ciencias Naturales y Museo. Área Zoología; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Jimenez, Jaime E.. Universidad de Magallanes; ChileFil: Lammertink, J. Martjan. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Nordeste. Instituto de Biología Subtropical. Instituto de Biología Subtropical - Nodo Posadas | Universidad Nacional de Misiones. Instituto de Biología Subtropical. Instituto de Biología Subtropical - Nodo Posadas; ArgentinaFil: Lopez, F.. Universidad Nacional de La Pampa; ArgentinaFil: Nuñez Montellano, Maria Gabriela. Consejo Nacional de Investigaciones Científicas y Técnicas. Instituto de Ciencias de la Tierra y Ambientales de La Pampa. Universidad Nacional de La Pampa. Facultad de Ciencias Exactas y Naturales. Instituto de Ciencias de la Tierra y Ambientales de La Pampa; ArgentinaFil: de la Peña, Martín. No especifíca;Fil: Rivera, Luis Osvaldo. Universidad Nacional de Jujuy. Instituto de Ecorregiones Andinas. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Salta. Instituto de Ecorregiones Andinas; ArgentinaFil: Vivanco, Constanza Guadalupe. Universidad Nacional de Jujuy. Instituto de Ecorregiones Andinas. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Salta. Instituto de Ecorregiones Andinas; ArgentinaFil: Santillán, Miguel. Museo de Historia Natural de La Pampa; ArgentinaFil: Soto, G.. Cornell University; Estados UnidosFil: Vergara, P.. Universidad de Santiago de Chile; ChileFil: Politi, Natalia. University of North Texas; Estados Unido

Using ant colony optimization for routing in microprocesors

Power consumption is an important constraint on VLSI systems. With the advancement in technology, it is now possible to pack a large range of functionalities into VLSI devices. Hence it is important to find out ways to utilize these functionalities with optimized power consumption. This work focuses on curbing power consumption at the design stage. This work emphasizes minimizing active power consumption by minimizing the load capacitance of the chip. Capacitance of wires and vias can be minimized using Ant Colony Optimization (ACO) algorithms. ACO provides a multi agent framework for combinatorial optimization problems and hence is used to handle multiple constraints of minimizing wire-length and vias to achieve the goal of minimizing capacitance and hence power consumption. The ACO developed here is able to achieve an 8% reduction of wire-length and 7% reduction in vias thereby providing a 7% reduction in total capacitance, compared to other state of the art routers