Morphology and phylogenetic relationships of a remarkable new genus and two new species of Neotropical freshwater stingrays from the Amazon basin (Chondrichthyes: Potamotrygonidae)

The morphology and phylogenetic relationships of a new genus and two new species of Neotropical freshwater stingrays, family Potamotrygonidae, are investigated and described in detail. The new genus, Heliotrygon, n. gen., and its two new species, Heliotrygon gomesi, n. sp. (type-species) and Heliotrygon rosai, n. sp., are compared to all genera and species of potamotrygonids, based on revisions in progress. Some of the derived features of Heliotrygon include its unique disc proportions (disc highly circular, convex anteriorly at snout region, its width and length very similar), extreme subdivision of suborbital canal (forming a complex honeycomb-like pattern anterolaterally on disc), stout and triangular pelvic girdle, extremely reduced caudal sting, basibranchial copula with very slender and acute anterior extension, and precerebral and frontoparietal fontanellae of about equal width, tapering very little posteriorly. Both new species can be distinguished by their unique color patterns: Heliotrygon gomesi is uniform gray to light tan or brownish dorsally, without distinct patterns, whereas Heliotrygon rosai is characterized by numerous white to creamy-white vermiculate markings over a light brown, tan or gray background color. Additional proportional characters that may further distinguish both species are also discussed. Morphological descriptions are provided for dermal denticles, ventral lateral-line canals, skeleton, and cranial, hyoid and mandibular muscles of Heliotrygon, which clearly corroborate it as the sister group of Paratrygon. Both genera share numerous derived features of the ventral lateral-line canals, neurocranium, scapulocoracoid, pectoral basals, clasper morphology, and specific patterns of the adductor mandibulae and spiracularis medialis muscles. Potamotrygon and Plesiotrygon are demonstrated to share derived characters of their ventral lateral-line canals, in addition to the presence of angular cartilages. Our morphological phylogeny is further corroborated by a molecular phylogenetic analysis of cytochrome b based on four sequences (637 base pairs in length), representing two distinct haplotypes for Heliotrygon gomesi. Parsimony analysis produced a single most parsimonious tree revealing Heliotrygon and Paratrygon as sister taxa (boot-strap proportion of 70%), which together are the sister group to a clade including Plesiotrygon and species of Potamotrygon. These unusual stingrays highlight that potamotrygonid diversity, both in terms of species composition and undetected morphological and molecular patterns, is still poorly known.

Seeking for simplicity in complex networks

Complex networks can be understood as graphs whose connectivity properties deviate from those of regular or near-regular graphs, which are understood as being ""simple"". While a great deal of the attention so far dedicated to complex networks has been duly driven by the ""complex"" nature of these structures, in this work we address the identification of their simplicity. The basic idea is to seek for subgraphs whose nodes exhibit similar measurements. This approach paves the way for complementing the characterization of networks, including results suggesting that the protein-protein interaction networks, and to a lesser extent also the Internet, may be getting simpler over time. Copyright (C) EPLA, 2009

Border trees of complex networks

The comprehensive characterization of the structure of complex networks is essential to understand the dynamical processes which guide their evolution. The discovery of the scale-free distribution and the small-world properties of real networks were fundamental to stimulate more realistic models and to understand important dynamical processes related to network growth. However, the properties of the network borders (nodes with degree equal to 1), one of its most fragile parts, remained little investigated and understood. The border nodes may be involved in the evolution of structures such as geographical networks. Here we analyze the border trees of complex networks, which are defined as the subgraphs without cycles connected to the remainder of the network (containing cycles) and terminating into border nodes. In addition to describing an algorithm for identification of such tree subgraphs, we also consider how their topological properties can be quantified in terms of their depth and number of leaves. We investigate the properties of border trees for several theoretical models as well as real-world networks. Among the obtained results, we found that more than half of the nodes of some real-world networks belong to the border trees. A power-law with cut-off was observed for the distribution of the depth and number of leaves of the border trees. An analysis of the local role of the nodes in the border trees was also performed.

New and improved results for packing identical unitary radius circles within triangles, rectangles and strips

The focus of study in this paper is the class of packing problems. More specifically, it deals with the placement of a set of N circular items of unitary radius inside an object with the aim of minimizing its dimensions. Differently shaped containers are considered, namely circles, squares, rectangles, strips and triangles. By means of the resolution of non-linear equations systems through the Newton-Raphson method, the herein presented algorithm succeeds in improving the accuracy of previous results attained by continuous optimization approaches up to numerical machine precision. The computer implementation and the data sets are available at http://www.ime.usp.br/similar to egbirgin/packing/. (C) 2009 Elsevier Ltd, All rights reserved.

Proximal methods for nonlinear programming: double regularization and inexact subproblems

This paper describes the first phase of a project attempting to construct an efficient general-purpose nonlinear optimizer using an augmented Lagrangian outer loop with a relative error criterion, and an inner loop employing a state-of-the art conjugate gradient solver. The outer loop can also employ double regularized proximal kernels, a fairly recent theoretical development that leads to fully smooth subproblems. We first enhance the existing theory to show that our approach is globally convergent in both the primal and dual spaces when applied to convex problems. We then present an extensive computational evaluation using the CUTE test set, showing that some aspects of our approach are promising, but some are not. These conclusions in turn lead to additional computational experiments suggesting where to next focus our theoretical and computational efforts.

Second-order negative-curvature methods for box-constrained and general constrained optimization

A Nonlinear Programming algorithm that converges to second-order stationary points is introduced in this paper. The main tool is a second-order negative-curvature method for box-constrained minimization of a certain class of functions that do not possess continuous second derivatives. This method is used to define an Augmented Lagrangian algorithm of PHR (Powell-Hestenes-Rockafellar) type. Convergence proofs under weak constraint qualifications are given. Numerical examples showing that the new method converges to second-order stationary points in situations in which first-order methods fail are exhibited.

Approximation algorithms and hardness results for the clique packing problem

For a fixed family F of graphs, an F-packing in a graph G is a set of pairwise vertex-disjoint subgraphs of G, each isomorphic to an element of F. Finding an F-packing that maximizes the number of covered edges is a natural generalization of the maximum matching problem, which is just F = {K(2)}. In this paper we provide new approximation algorithms and hardness results for the K(r)-packing problem where K(r) = {K(2), K(3,) . . . , K(r)}. We show that already for r = 3 the K(r)-packing problem is APX-complete, and, in fact, we show that it remains so even for graphs with maximum degree 4. On the positive side, we give an approximation algorithm with approximation ratio at most 2 for every fixed r. For r = 3, 4, 5 we obtain better approximations. For r = 3 we obtain a simple 3/2-approximation, achieving a known ratio that follows from a more involved algorithm of Halldorsson. For r = 4, we obtain a (3/2 + epsilon)-approximation, and for r = 5 we obtain a (25/14 + epsilon)-approximation. (C) 2008 Elsevier B.V. All rights reserved.

Minimizing the object dimensions in circle and sphere packing problems

Given a fixed set of identical or different-sized circular items, the problem we deal with consists on finding the smallest object within which the items can be packed. Circular, triangular, squared, rectangular and also strip objects are considered. Moreover, 2D and 3D problems are treated. Twice-differentiable models for all these problems are presented. A strategy to reduce the complexity of evaluating the models is employed and, as a consequence, instances with a large number of items can be considered. Numerical experiments show the flexibility and reliability of the new unified approach. (C) 2007 Elsevier Ltd. All rights reserved.

Structured minimal-memory inexact quasi-Newton method and secant preconditioners for augmented Lagrangian optimization

Augmented Lagrangian methods for large-scale optimization usually require efficient algorithms for minimization with box constraints. On the other hand, active-set box-constraint methods employ unconstrained optimization algorithms for minimization inside the faces of the box. Several approaches may be employed for computing internal search directions in the large-scale case. In this paper a minimal-memory quasi-Newton approach with secant preconditioners is proposed, taking into account the structure of Augmented Lagrangians that come from the popular Powell-Hestenes-Rockafellar scheme. A combined algorithm, that uses the quasi-Newton formula or a truncated-Newton procedure, depending on the presence of active constraints in the penalty-Lagrangian function, is also suggested. Numerical experiments using the Cute collection are presented.

Improving ultimate convergence of an augmented Lagrangian method

Optimization methods that employ the classical Powell-Hestenes-Rockafellar augmented Lagrangian are useful tools for solving nonlinear programming problems. Their reputation decreased in the last 10 years due to the comparative success of interior-point Newtonian algorithms, which are asymptotically faster. In this research, a combination of both approaches is evaluated. The idea is to produce a competitive method, being more robust and efficient than its `pure` counterparts for critical problems. Moreover, an additional hybrid algorithm is defined, in which the interior-point method is replaced by the Newtonian resolution of a Karush-Kuhn-Tucker (KKT) system identified by the augmented Lagrangian algorithm. The software used in this work is freely available through the Tango Project web page:http://www.ime.usp.br/similar to egbirgin/tango/.

Augmented Lagrangian methods under the constant positive linear dependence constraint qualification

Two Augmented Lagrangian algorithms for solving KKT systems are introduced. The algorithms differ in the way in which penalty parameters are updated. Possibly infeasible accumulation points are characterized. It is proved that feasible limit points that satisfy the Constant Positive Linear Dependence constraint qualification are KKT solutions. Boundedness of the penalty parameters is proved under suitable assumptions. Numerical experiments are presented.

Tilt-critical algebras of tame type

Let A be a finite dimensional k-algebra over an algebraically closed field. Assume A=kQ/I where Q is a quiver without oriented cycles. We say that A is tilt-critical if it is not tilted but every proper convex subcategory of A is tilted. We describe the tilt-critical algebras which are strongly simply connected and tame.

On the Multiplicity of Orthogonal Geodesics in Riemannian Manifold With Concave Boundary. Applications to Brake Orbits and Homoclinics

Let (M, g) be a complete Riemannian Manifold, Omega subset of M an open subset whose closure is diffeomorphic to an annulus. If partial derivative Omega is smooth and it satisfies a strong concavity assumption, then it is possible to prove that there are at least two geometrically distinct geodesics in (Omega) over bar = Omega boolean OR partial derivative Omega starting orthogonally to one connected component of partial derivative Omega and arriving orthogonally onto the other one. The results given in [6] allow to obtain a proof of the existence of two distinct homoclinic orbits for an autonomous Lagrangian system emanating from a nondegenerate maximum point of the potential energy, and a proof of the existence of two distinct brake orbits for a. class of Hamiltonian systems. Under a further symmetry assumption, it is possible to show the existence of at least dim(M) pairs of geometrically distinct geodesics as above, brake orbits and homoclinics.

Asymmetric Ramsey Properties of Random Graphs Involving Cliques

Consider the following problem: Forgiven graphs G and F(1),..., F(k), find a coloring of the edges of G with k colors such that G does not contain F; in color i. Rodl and Rucinski studied this problem for the random graph G,,, in the symmetric case when k is fixed and F(1) = ... = F(k) = F. They proved that such a coloring exists asymptotically almost surely (a.a.s.) provided that p <= bn(-beta) for some constants b = b(F,k) and beta = beta(F). This result is essentially best possible because for p >= Bn(-beta), where B = B(F, k) is a large constant, such an edge-coloring does not exist. Kohayakawa and Kreuter conjectured a threshold function n(-beta(F1,..., Fk)) for arbitrary F(1), ..., F(k). In this article we address the case when F(1),..., F(k) are cliques of different sizes and propose an algorithm that a.a.s. finds a valid k-edge-coloring of G(n,p) with p <= bn(-beta) for some constant b = b(F(1),..., F(k)), where beta = beta(F(1),..., F(k)) as conjectured. With a few exceptions, this algorithm also works in the general symmetric case. We also show that there exists a constant B = B(F,,..., Fk) such that for p >= Bn(-beta) the random graph G(n,p) a.a.s. does not have a valid k-edge-coloring provided the so-called KLR-conjecture holds. (C) 2008 Wiley Periodicals, Inc. Random Struct. Alg., 34, 419-453, 2009

On Approximate KKT Condition and its Extension to Continuous Variational Inequalities

In this work, we introduce a necessary sequential Approximate-Karush-Kuhn-Tucker (AKKT) condition for a point to be a solution of a continuous variational inequality, and we prove its relation with the Approximate Gradient Projection condition (AGP) of Garciga-Otero and Svaiter. We also prove that a slight variation of the AKKT condition is sufficient for a convex problem, either for variational inequalities or optimization. Sequential necessary conditions are more suitable to iterative methods than usual punctual conditions relying on constraint qualifications. The AKKT property holds at a solution independently of the fulfillment of a constraint qualification, but when a weak one holds, we can guarantee the validity of the KKT conditions.