Distinguishing links up to link-homotopy by algebraic methods

In this paper we provide a complete algebraic invariant of link-homotopy, that is, an algebraic invariant that distinguishes two links if and only if they are link-homotopic. The paper establishes a connection between the ""peripheral structures"" approach to link-homotopy taken by Milnor, Levine and others, and the string link action approach taken by Habegger and Lin. (C) 2009 Elsevier B.V. All rights reserved.

Numerical prediction of three-dimensional time-dependent viscoelastic extrudate swell using differential and algebraic models

This study investigates the numerical simulation of three-dimensional time-dependent viscoelastic free surface flows using the Upper-Convected Maxwell (UCM) constitutive equation and an algebraic explicit model. This investigation was carried out to develop a simplified approach that can be applied to the extrudate swell problem. The relevant physics of this flow phenomenon is discussed in the paper and an algebraic model to predict the extrudate swell problem is presented. It is based on an explicit algebraic representation of the non-Newtonian extra-stress through a kinematic tensor formed with the scaled dyadic product of the velocity field. The elasticity of the fluid is governed by a single transport equation for a scalar quantity which has dimension of strain rate. Mass and momentum conservations, and the constitutive equation (UCM and algebraic model) were solved by a three-dimensional time-dependent finite difference method. The free surface of the fluid was modeled using a marker-and-cell approach. The algebraic model was validated by comparing the numerical predictions with analytic solutions for pipe flow. In comparison with the classical UCM model, one advantage of this approach is that computational workload is substantially reduced: the UCM model employs six differential equations while the algebraic model uses only one. The results showed stable flows with very large extrudate growths beyond those usually obtained with standard differential viscoelastic models. (C) 2010 Elsevier Ltd. All rights reserved.

ON AMINO ACID AND CODON ASSIGNMENT IN ALGEBRAIC MODELS FOR THE GENETIC CODE

We give a list of all possible schemes for performing amino acid and codon assignments in algebraic models for the genetic code, which are consistent with a few simple symmetry principles, in accordance with the spirit of the algebraic approach to the evolution of the genetic code proposed by Hornos and Hornos. Our results are complete in the sense of covering all the algebraic models that arise within this approach, whether based on Lie groups/Lie algebras, on Lie superalgebras or on finite groups.

An application of lattice basis reduction to polynomial identities for algebraic structures

The authors` recent classification of trilinear operations includes, among other cases, a fourth family of operations with parameter q epsilon Q boolean OR {infinity}, and weakly commutative and weakly anticommutative operations. These operations satisfy polynomial identities in degree 3 and further identities in degree 5. For each operation, using the row canonical form of the expansion matrix E to find the identities in degree 5 gives extremely complicated results. We use lattice basis reduction to simplify these identities: we compute the Hermite normal form H of E(t), obtain a basis of the nullspace lattice from the last rows of a matrix U for which UE(t) = H, and then use the LLL algorithm to reduce the basis. (C) 2008 Elsevier Inc. All rights reserved.

ALGEBRAIC AND GEOMETRIC THEORY OF THE TOPOLOGICAL RING OF COLOMBEAU GENERALIZED FUNCTIONS

We continue the investigation of the algebraic and topological structure of the algebra of Colombeau generalized functions with the aim of building up the algebraic basis for the theory of these functions. This was started in a previous work of Aragona and Juriaans, where the algebraic and topological structure of the Colombeau generalized numbers were studied. Here, among other important things, we determine completely the minimal primes of (K) over bar and introduce several invariants of the ideals of 9(Q). The main tools we use are the algebraic results obtained by Aragona and Juriaans and the theory of differential calculus on generalized manifolds developed by Aragona and co-workers. The main achievement of the differential calculus is that all classical objects, such as distributions, become Cl-functions. Our purpose is to build an independent and intrinsic theory for Colombeau generalized functions and place them in a wider context.

Polar orthogonal representations of real reductive algebraic groups

We prove that a polar orthogonal representation of a real reductive algebraic group has the same closed orbits as the isotropy representation of a pseudo-Riemannian symmetric space. We also develop a partial structural theory of polar orthogonal representations of real reductive algebraic groups which slightly generalizes some results of the structural theory of real reductive Lie algebras. (c) 2008 Elsevier Inc. All rights reserved.

Algebraic Bol loops

In this paper, we study the category of algebraic Bol loops over an algebraically closed field of definition. On the one hand, we apply techniques from the theory of algebraic groups in order to prove structural theorems for this category. On the other hand, we present some examples showing that these loops lack some nice properties of algebraic groups; for example, we construct local algebraic Bol loops which are not birationally equivalent to global algebraic loops.

An algebraic theory for generalized Jordan chains and partial signatures in the Lagrangian Grassmannian

We discuss an algebraic theory for generalized Jordan chains and partial signatures, that are invariants associated to sequences of symmetric bilinear forms on a vector space. We introduce an intrinsic notion of partial signatures in the Lagrangian Grassmannian of a symplectic space that does not use local coordinates, and we give a formula for the Maslov index of arbitrary real analytic paths in terms of partial signatures.

Forest-obligate Sabethes mosquitoes suggest palaeoecological perturbations

The origin of tropical forest diversity has been hotly debated for decades. Although specific mechanisms vary, many such explanations propose some vicariance in the distribution of species during glacial cycles and several have been supported by genetic evidence in Neotropical taxa. However, no consensus exists with regard to the extent or time frame of the vicariance events. Here, we analyse the cytochrome oxidase II mitochondrial gene of 250 Sabethes albiprivus B mosquitoes sampled from western Sao Paulo in Brazil. There was very low population structuring among collection sites (Phi(ST) = 0.03, P = 0.04). Historic demographic analyses and the contemporary geographic distribution of genetic diversity suggest that the populations sampled are not at demographic equilibrium. Three distinct mitochondrial clades were observed in the samples, one of which differed significantly in its geographic distribution relative to the other two within a small sampling area (similar to 70 x 35 km). This fact, supported by the inability of maximum likelihood analyses to achieve adequate fits to simple models for the population demography of the species, suggests a more complex history, possibly involving disjunct forest refugia. This hypothesis is supported by a genetic signal of recent population growth, which is expected if population sizes of this forest-obligate insect increased during the forest expansions that followed glacial periods. Although a time frame cannot be reliably inferred for the vicariance event leading to the three genetic clades, molecular clock estimates place this at similar to 1 Myr before present.

Short report: Historical analysis of a near disaster: Anopheles gambiae in Brazil

Attributed to human-mediated dispersal, a species of the Anopheles gambiae complex invaded northeastern Brazil in 1930. This event is considered unique among the intercontinental introductions of disease vectors and the most serious one: ""Few threats to the future health of the Americas have equalled that inherent in the invasion of Brazil, in 1930, by Anopheles gambiae."" Because it was only in the 1960s that An. gambiae was recognized as a species complex now including seven species, the precise species identity of the Brazilian invader remains a mystery. Here we used historical DNA analysis of museum specimens, collected at the time of invasion from Brazil, and aimed at the identification of the Brazilian invader. Our results identify the arid-adapted Anopheles arabiensis as being the actual invading species. Establishing the identity of the species, in addition to being of intrinsic historical interest, can inform future threats of this sort especially in a changing environment. Furthermore, these results highlight the potential danger of human-mediated range expansions of insect disease vectors and the importance of museum collections in retrieving historical information.

Effects of roads, topography, and land use on forest cover dynamics in the Brazilian Atlantic Forest

Roads and topography can determine patterns of land use and distribution of forest cover, particularly in tropical regions. We evaluated how road density, land use, and topography affected forest fragmentation, deforestation and forest regrowth in a Brazilian Atlantic Forest region near the city of Sao Paulo. We mapped roads and land use/land cover for three years (1962, 1981 and 2000) from historical aerial photographs, and summarized the distribution of roads, land use/land cover and topography within a grid of 94 non-overlapping 100 ha squares. We used generalized least squares regression models for data analysis. Our models showed that forest fragmentation and deforestation depended on topography, land use and road density, whereas forest regrowth depended primarily on land use. However, the relationships between these variables and forest dynamics changed in the two studied periods; land use and slope were the strongest predictors from 1962 to 1981, and past (1962) road density and land use were the strongest predictors for the following period (1981-2000). Roads had the strongest relationship with deforestation and forest fragmentation when the expansions of agriculture and buildings were limited to already deforested areas, and when there was a rapid expansion of development, under influence of Sao Paulo city. Furthermore, the past(1962)road network was more important than the recent road network (1981) when explaining forest dynamics between 1981 and 2000, suggesting a long-term effect of roads. Roads are permanent scars on the landscape and facilitate deforestation and forest fragmentation due to increased accessibility and land valorization, which control land-use and land-cover dynamics. Topography directly affected deforestation, agriculture and road expansion, mainly between 1962 and 1981. Forest are thus in peril where there are more roads, and long-term conservation strategies should consider ways to mitigate roads as permanent landscape features and drivers facilitators of deforestation and forest fragmentation. (C) 2009 Elsevier B.V. All rights reserved.

C(0) and bi-Lipschitz K-equivalence of mappings

In this paper we investigate the classification of mappings up to K-equivalence. We give several results of this type. We study semialgebraic deformations up to semialgebraic C(0) K-equivalence and bi-Lipschitz K-equivalence. We give an algebraic criterion for bi-Lipschitz K-triviality in terms of semi-integral closure (Theorem 3.5). We also give a new proof of a result of Nishimura: we show that two germs of smooth mappings f, g : R(n) -> R(n), finitely determined with respect to K-equivalence are C(0)-K-equivalent if and only if they have the same degree in absolute value.

The curve selection lemma and the Morse-Sard theorem

We use an inequality due to Bochnak and Lojasiewicz, which follows from the Curve Selection Lemma of real algebraic geometry in order to prove that, given a C(r) function f : U subset of R(m) -> R, we have lim(y -> xy is an element of crit(f)) vertical bar f(y) - f(x)vertical bar/vertical bar y - x vertical bar(r) = 0, for all x is an element of crit(f)` boolean AND U, where crit( f) = {x is an element of U vertical bar df ( x) = 0}. This shows that the so-called Morse decomposition of the critical set, used in the classical proof of the Morse-Sard theorem, is not necessary: the conclusion of the Morse decomposition lemma holds for the whole critical set. We use this result to give a simple proof of the classical Morse-Sard theorem ( with sharp differentiability assumptions).

Invariant theory and reversible-equivariant vector fields

In this paper we present results for the systematic study of reversible-equivariant vector fields - namely, in the simultaneous presence of symmetries and reversing symmetries - by employing algebraic techniques from invariant theory for compact Lie groups. The Hilbert-Poincare series and their associated Molien formulae are introduced,and we prove the character formulae for the computation of dimensions of spaces of homogeneous anti-invariant polynomial functions and reversible-equivariant polynomial mappings. A symbolic algorithm is obtained for the computation of generators for the module of reversible-equivariant polynomial mappings over the ring of invariant polynomials. We show that this computation can be obtained directly from a well-known situation, namely from the generators of the ring of invariants and the module of the equivariants. (C) 2008 Elsevier B.V, All rights reserved.

Resampling Strategies for Deforming MLS Surfaces

Moving-least-squares (MLS) surfaces undergoing large deformations need periodic regeneration of the point set (point-set resampling) so as to keep the point-set density quasi-uniform. Previous work by the authors dealt with algebraic MLS surfaces, and proposed a resampling strategy based on defining the new points at the intersections of the MLS surface with a suitable set of rays. That strategy has very low memory requirements and is easy to parallelize. In this article new resampling strategies with reduced CPU-time cost are explored. The basic idea is to choose as set of rays the lines of a regular, Cartesian grid, and to fully exploit this grid: as data structure for search queries, as spatial structure for traversing the surface in a continuation-like algorithm, and also as approximation grid for an interpolated version of the MLS surface. It is shown that in this way a very simple and compact resampling technique is obtained, which cuts the resampling cost by half with affordable memory requirements.