Structure and magnetic properties of polydisperse ferrofluids: a molecular dynamics study

We study by Langevin molecular dynamics simulations systematically the influence of polydispersity in the particle size, and subsequently in the dipole moment, on the physical properties of ferrofluids. The polydispersity is in a first approximation modeled by a bidisperse system that consists of small and large particles at different ratios of their volume fractions. In the first part of our investigations the total volume fraction of the system is fixed, and the volume fraction phi(L) of the large particles is varied. The initial susceptibility chi and magnetization curve of the systems show a strong dependence on the value of phi(L). With the increase of phi(L), the magnetization M of the system has a much faster increment at weak fields, and thus leads to a larger chi. We performed a cluster analysis that indicates that this is due to the aggregation of the large particles in the systems. The average size of these clusters increases with increasing phi(L). In the second part of our investigations, we fixed the volume fraction of the large particles, and increased the volume fraction phi(S) of the small particles in order to study their influence on the chain formation of the large ones. We found that the average aggregate size formed by large particles decreases when phi(S) is increased, demonstrating a significant effect of the small particles on the structural properties of the system. A topological analysis of the structure reveals that the majority of the small particles remain nonaggregated. Only a small number of them are attracted to the ends of the chains formed by large particles.

Identifying the Open-Closed Field Line Boundary

Of all the various definitions of the polar cap boundary that have been used in the past, the most physically meaningful and significant is the boundary between open and closed field lines. Locating this boundary is very important as it defines which regions and phenomena are on open field lines and which are on closed. This usually has fundamental implications for the mechanisms invoked. Unfortunately, the open-closed boundary is usually very difficult to identify, particularly where it maps to an active reconnection site. This paper looks at the topological reconnection classes that can take place, both at the magnetopause and in the cross-tail current sheet and discusses the implications for identifying the open-closed boundary when reconnection is giving velocity filter dispersion of signatures. On the dayside, it is shown that the dayside boundary plasma sheet and low-latitude boundary layer precipitations are well explained as being on open field lines, energetic ions being present because of reflection of central plasma sheet ions off the two Alfvén waves launched by the reconnection site (the outer one of which is the magnetopause). This also explains otherwise anomalous features of the dayside convection pattern in the cusp region. On the nightside, similar considerations place the open-closed boundary somewhat poleward of the velocity-dispersed ion structures which are a signature of the plasma sheet boundary layer ion flows in the tail.

Interaction of adult human neural crest-derived stem cells with a nanoporous titanium surface is sufficient to induce their osteogenic differentiation

Osteogenic differentiation of various adult stem cell populations such as neural crest-derived stem cells is of great interest in the context of bone regeneration. Ideally, exogenous differentiation should mimic an endogenous differentiation process, which is partly mediated by topological cues. To elucidate the osteoinductive potential of porous substrates with different pore diameters (30 nm, 100 nm), human neural crest-derived stem cells isolated from the inferior nasal turbinate were cultivated on the surface of nanoporous titanium covered membranes without additional chemical or biological osteoinductive cues. As controls, flat titanium without any topological features and osteogenic medium was used. Cultivation of human neural crest-derived stem cells on 30 nm pores resulted in osteogenic differentiation as demonstrated by alkaline phosphatase activity after seven days as well as by calcium deposition after 3 weeks of cultivation. In contrast, cultivation on flat titanium and on membranes equipped with 100 nm pores was not sufficient to induce osteogenic differentiation. Moreover, we demonstrate an increase of osteogenic transcripts including Osterix, Osteocalcin and up-regulation of Integrin β1 and α2 in the 30 nm pore approach only. Thus, transplantation of stem cells pre-cultivated on nanostructured implants might improve the clinical outcome by support of the graft adherence and acceleration of the regeneration process.

Uniqueness of signature for simple curves

We propose a topological approach to the problem of determining a curve from its iterated integrals. In particular, we prove that a family of terms in the signature series of a two dimensional closed curve with finite p-variation, 1≤p<2, are in fact moments of its winding number. This relation allows us to prove that the signature series of a class of simple non-smooth curves uniquely determine the curves. This implies that outside a Chordal SLEκ null set, where 0<κ≤4, the signature series of curves uniquely determine the curves. Our calculations also enable us to express the Fourier transform of the n-point functions of SLE curves in terms of the expected signature of SLE curves. Although the techniques used in this article are deterministic, the results provide a platform for studying SLE curves through the signatures of their sample paths.

Counting in Egyptian children with Down Syndrome

This exploratory study is concerned with the performance of Egyptian children with Down syndrome on counting and error detection tasks and investigates how these children acquire counting. Observations and interviews were carried out to collect further information about their performance in a class context. Qualitative and quantitative analysis suggested a notable deficit in counting in Egyptian children with Down syndrome with none of the children able to recite the number string up to ten or count a set of five objects correctly. They performed less well on tasks which added more load on memory. The tentative finding of this exploratory study supported previous research findings that children with Down syndrome acquire counting by rote and links this with their learning experiences.

Cheaters in mutualism networks

Mutualism-network studies assume that all interacting species are mutualistic partners and consider that all links are of one kind. However, the influence of different types of links, such as cheating links, on network organization remains unexplored. We studied two flower-visitation networks (Malpighiaceae and Bignoniaceae and their flower visitors), and divide the types of link into cheaters (i.e. robbers and thieves of flower rewards) and effective pollinators. We investigated if there were topological differences among networks with and without cheaters, especially with respect to nestedness and modularity. The Malpighiaceae network was nested, but not modular, and it was dominated by pollinators and had much fewer cheater species than Bignoniaceae network (28% versus 75%). The Bignoniaceae network was mainly a plant-cheater network, being modular because of the presence of pollen robbers and showing no nestedness. In the Malpighiaceae network, removal of cheaters had no major consequences for topology. In contrast, removal of cheaters broke down the modularity of the Bignoniaceae network. As cheaters are ubiquitous in all mutualisms, the results presented here show that they have a strong impact upon network topology.

What makes a species central in a cleaning mutualism network?

Mutualisms often form networks of interacting species, characterized by the existence of a central core of species that potentially drive the ecology and the evolution of the whole community. Centrality measures allow quantification of how central or peripheral a species is within a network, thus informing about the role of each species in network organization, dynamics, and stability. In the present study we addressed the question whether the structural position of species in the network (i.e. their topological importance) relates to their ecological traits. We studied interactions between cleaner and client reef fishes to identify central and peripheral species within a mutualistic network, and investigated five ecological correlates. We used three measures to estimate the level of centrality of a species for distinct structural patterns, such as the number of interactions and the structural proximity to other species. Through the use of a principal component analysis (PCA) we observed that the centrality measures were highly correlated (92.5%) in the studied network, which indicates that the same species plays a similar role for the different structural patterns. Three cleaner and ten client species had positive values of centrality, which suggests that these species are modulating ecological and evolutionary dynamics within the network. Higher centralities were related to higher abundances and feeding habits for client fishes, but not for cleaners. The high correlation between centrality measures in the present study is likely related to the nested structure of the cleaning network. The cleaner species` set, by having central species that are not necessarily the most abundant ones, bears potentially more vulnerable points for network cohesiveness. Additionally, the present study generalizes previous findings for plant-animal mutualisms, as it shows that the structure of marine mutualisms is also related to a complex interplay between abundance and niche-related features.

The nested assembly of individual-resource networks

P>1. Much of the current understanding of ecological systems is based on theory that does not explicitly take into account individual variation within natural populations. However, individuals may show substantial variation in resource use. This variation in turn may be translated into topological properties of networks that depict interactions among individuals and the food resources they consume (individual-resource networks). 2. Different models derived from optimal diet theory (ODT) predict highly distinct patterns of trophic interactions at the individual level that should translate into distinct network topologies. As a consequence, individual-resource networks can be useful tools in revealing the incidence of different patterns of resource use by individuals and suggesting their mechanistic basis. 3. In the present study, using data from several dietary studies, we assembled individual-resource networks of 10 vertebrate species, previously reported to show interindividual diet variation, and used a network-based approach to investigate their structure. 4. We found significant nestedness, but no modularity, in all empirical networks, indicating that (i) these populations are composed of both opportunistic and selective individuals and (ii) the diets of the latter are ordered as predictable subsets of the diets of the more opportunistic individuals. 5. Nested patterns are a common feature of species networks, and our results extend its generality to trophic interactions at the individual level. This pattern is consistent with a recently proposed ODT model, in which individuals show similar rank preferences but differ in their acceptance rate for alternative resources. Our findings therefore suggest a common mechanism underlying interindividual variation in resource use in disparate taxa.

Coding behavioural data for cladistic analysis: using dynamic homology without parsimony

Many of the controversies around the concept of homology rest on the subjectivity inherent to primary homology propositions. Dynamic homology partially solves this problem, but there has been up to now scant application of it outside of the molecular domain. This is probably because morphological and behavioural characters are rich in properties, connections and qualities, so that there is less space for conflicting character delimitations. Here we present a new method for the direct optimization of behavioural data, a method that relies on the richness of this database to delimit the characters, and on dynamic procedures to establish character state identity. We use between-species congruence in the data matrix and topological stability to choose the best cladogram. We test the methodology using sequences of predatory behaviour in a group of spiders that evolved the highly modified predatory technique of spitting glue onto prey. The cladogram recovered is fully compatible with previous analyses in the literature, and thus the method seems consistent. Besides the advantage of enhanced objectivity in character proposition, the new procedure allows the use of complex, context-dependent behavioural characters in an evolutionary framework, an important step towards the practical integration of the evolutionary and ecological perspectives on diversity. (C) The Willi Hennig Society 2010.

The analytic torsion of a cone over an odd dimensional manifold

We study the analytic torsion of a cone over an orientable odd dimensional compact connected Riemannian manifold W. We prove that the logarithm of the analytic torsion of the cone decomposes as the sum of the logarithm of the root of the analytic torsion of the boundary of the cone, plus a topological term, plus a further term that is a rational linear combination of local Riemannian invariants of the boundary. We show that this last term coincides with the anomaly boundary term appearing in the Cheeger Muller theorem [3, 2] for a manifold with boundary, according to Bruning and Ma (2006) [5]. We also prove Poincare duality for the analytic torsion of a cone. (C) 2010 Elsevier B.V. All rights reserved.

ROOT PROBLEM FOR CONVENIENT MAPS

In this paper we study when the minimal number of roots of the so-called convenient maps horn two-dimensional CW complexes into closed surfaces is zero We present several necessary and sufficient conditions for such a map to be root free Among these conditions we have the existence of specific fittings for the homomorphism induced by the map on the fundamental groups, existence of the so-called mutation of a specific homomorphism also induced by the map, and existence of particular solutions of specific systems of equations on free groups over specific subgroups

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.

ON NONSYMMETRIC THEOREMS FOR (H, G)-COINCIDENCES

Let X be a compact Hausdorff space, phi: X -> S(n) a continuous map into the n-sphere S(n) that induces a nonzero homomorphism phi*: H(n)(S(n); Z(p)) -> H(n)(X; Z(p)), Y a k-dimensional CW-complex and f: X -> a continuous map. Let G a finite group which acts freely on S`. Suppose that H subset of G is a normal cyclic subgroup of a prime order. In this paper, we define and we estimate the cohomological dimension of the set A(phi)(f, H, G) of (H, G)-coincidence points of f relative to phi.

On the Fucik spectrum of the Laplacian on a torus

We study the Fucik spectrum of the Laplacian on a two-dimensional torus T(2). Exploiting the invariance properties of the domain T(2) with respect to translations we obtain a good description of large parts of the spectrum. In particular, for each eigenvalue of the Laplacian we will find an explicit global curve in the Fucik spectrum which passes through this eigenvalue; these curves are ordered, and we will show that their asymptotic limits are positive. On the other hand, using a topological index based on the mentioned group invariance, we will obtain a variational characterization of global curves in the Fucik spectrum; also these curves emanate from the eigenvalues of the Laplacian, and we will show that they tend asymptotically to zero. Thus, we infer that the variational and the explicit curves cannot coincide globally, and that in fact many curve crossings must occur. We will give a bifurcation result which partially explains these phenomena. (C) 2008 Elsevier Inc. All rights reserved.

Stability of gradient semigroups under perturbations

In this paper we prove that gradient-like semigroups (in the sense of Carvalho and Langa (2009 J. Diff. Eqns 246 2646-68)) are gradient semigroups (possess a Lyapunov function). This is primarily done to provide conditions under which gradient semigroups, in a general metric space, are stable under perturbation exploiting the known fact (see Carvalho and Langa (2009 J. Diff. Eqns 246 2646-68)) that gradient-like semigroups are stable under perturbation. The results presented here were motivated by the work carried out in Conley (1978 Isolated Invariant Sets and the Morse Index (CBMS Regional Conference Series in Mathematics vol 38) (RI: American Mathematical Society Providence)) for groups in compact metric spaces (see also Rybakowski (1987 The Homotopy Index and Partial Differential Equations (Universitext) (Berlin: Springer)) for the Morse decomposition of an invariant set for a semigroup on a compact metric space).