Pablo Moisset de Espanés

Complexities for Generalized Models of Self-Assembly

In this paper, we extend Rothemund and Winfrees examination of the tile complexity of tile self-assembly [6]. They provided a lower bound of Ω(log <i>N</i>/log log <i>N</i>) on the tile complexity of assembling an <i>N</i> × <i>N</i> square for almost all <i>N</i>. Adleman et al. [1] gave a construction which achieves this bound. We consider whether the tile complexity for self-assembly can be reduced through several natural generalizations of the model. One of our results is a tile set of size <i>O</i>(√log <i>N</i>) which assembles an <i>N</i> × <i>N</i> square in a model which allows flexible glue strength between non-equal glues (This was independently discovered in [3]). This result is matched by a lower bound dictated by Kolmogorov complexity. For three other generalizations, we show that the Ω(log <i>N</i>/log log <i>N</i>) lower bound applies to <i>N</i> × <i>N</i> squares. At the same time, we demonstrate that there are some other shapes for which these generalizations allow reduced tile sets. Specifically, for thin rectangles with length <i>N</i> and width <i>k</i>, we provide a tighter lower bound of Ω(<i>N</i>(1/<i>k</i>)/<i>k</i>) for the standard model, yet we also give a construction which achieves <i>O</i>(log <i>N</i>/log log <i>N</i>) complexity in a model in which the temperature of the tile system is adjusted during assembly. We also investigate the problem of verifying whether a given tile system uniquely assembles into a given shape, and show that this problem is NP-hard.

Combinatorial optimization problems in self-assembly

Self-assembly is the ubiquitous process by which simple objects autonomously assemble into intricate complexes. It has been suggested that intricate self-assembly processes will ultimately be used in circuit fabrication, nano-robotics, DNA computation, and amorphous computing. In this paper, we study two combinatorial optimization problems related to efficient self-assembly of shapes in the Tile Assembly Model of self-assembly proposed by Rothemund and Winfree [18]. The first is the Minimum Tile Set Problem, where the goal is to find the smallest tile system that uniquely produces a given shape. The second is the Tile Concentrations Problem, where the goal is to decide on the relative concentrations of different types of tiles so that a tile system assembles as quickly as possible. The first problem is akin to finding optimum program size, and the second to finding optimum running time for a program to assemble the shape.Self-assembly is the ubiquitous process by which simple objects autonomously assemble into intricate complexes. It has been suggested that intricate self-assembly processes will ultimately be used in circuit fabrication, nano-robotics, DNA computation, and amorphous computing. In this paper, we study two combinatorial optimization problems related to efficient self-assembly of shapes in the Tile Assembly Model of self-assembly proposed by Rothemund and Winfree [18]. The first is the Minimum Tile Set Problem, where the goal is to find the smallest tile system that uniquely produces a given shape. The second is the Tile Concentrations Problem, where the goal is to decide on the relative concentrations of different types of tiles so that a tile system assembles as quickly as possible. The first problem is akin to finding optimum program size, and the second to finding optimum running time for a program to assemble the shape.We prove that the first problem is NP-complete in general, and polynomial time solvable on trees and squares. In order to prove that the problem is in NP, we present a polynomial time algorithm to verify whether a given tile system uniquely produces a given shape. This algorithm is analogous to a program verifier for traditional computational systems, and may well be of independent interest. For the second problem, we present a polynomial time

Topological plasticity increases robustness of mutualistic networks

O(log n)

Niche partitioning due to adaptive foraging reverses effects of nestedness and connectance on pollination network stability.

-approximation algorithm that works for a large class of tile systems that we call partial order systems.

Toward minimum size self-assembled counters

1.u2002Earlier studies used static models to evaluate the responses of mutualistic networks to external perturbations. Two classes of dynamics can be distinguished in ecological networks; population dynamics, represented mainly by changes in species abundances, and topological dynamics, represented by changes in the architecture of the web. 2.u2002In this study, we model the temporal evolution of three empirical plant-pollination networks incorporating both population and topological dynamics. We test the hypothesis that topological plasticity, realized through the ability of animals to rewire their connections after depletion of host abundances, enhances tolerance of mutualistic networks to species loss. We also compared the performance of various rewiring rules in affecting robustness. 3.u2002The results show that topological plasticity markedly increased the robustness of mutualistic networks. Our analyses also revealed that network robustness reached maximum levels when animals with less host plant availability were more likely to rewire. Also, preferential attachment to richer host plants, that is, to plants exhibiting higher abundance and few exploiters, enhances robustness more than other rewiring alternatives. 4.u2002Our results highlight the potential role of topological plasticity in the robustness of mutualistic networks to species extinctions and suggest some plausible mechanisms by which the decisions of foragers may shape the collective dynamics of plant-pollinator systems.

Species traits and network structure predict the success and impacts of pollinator invasions

Much research debates whether properties of ecological networks such as nestedness and connectance stabilise biological communities while ignoring key behavioural aspects of organisms within these networks. Here, we computationally assess how adaptive foraging (AF) behaviour interacts with network architecture to determine the stability of plant-pollinator networks. We find that AF reverses negative effects of nestedness and positive effects of connectance on the stability of the networks by partitioning the niches among species within guilds. This behaviour enables generalist pollinators to preferentially forage on the most specialised of their plant partners which increases the pollination services to specialist plants and cedes the resources of generalist plants to specialist pollinators. We corroborate these behavioural preferences with intensive field observations of bee foraging. Our results show that incorporating key organismal behaviours with well-known biological mechanisms such as consumer-resource interactions into the analysis of ecological networks may greatly improve our understanding of complex ecosystems.

Phenology determines the robustness of plant–pollinator networks

DNA self-assembly is a promising paradigm for nanotechnology. In this paper we study the problem of finding tile systems of minimum size that assemble a given shape in the Tile Assembly Model, defined byRothemund and Winfree [14]. We present a tile system that assembles an N × ⌈log2 N⌉ rectangle in asymptotically optimal Θ(N) time. This tile system has only 7 tiles. Earlier constructions need at least 8 tiles [7]. We managed to reduce the number of tiles without increasing the assembly time. The new tile system works at temperature 3. n nThe new construction was found by the combination of exhaustive computerized search of the design space and manual adjustment of the search output.

Robust reconstruction of Barabási-Albert networks in the broadcast congested clique model

Species invasions constitute a major and poorly understood threat to plant–pollinator systems. General theory predicting which factors drive species invasion success and subsequent effects on native ecosystems is particularly lacking. We address this problem using a consumer–resource model of adaptive behavior and population dynamics to evaluate the invasion success of alien pollinators into plant–pollinator networks and their impact on native species. We introduce pollinator species with different foraging traits into network models with different levels of species richness, connectance, and nestedness. Among 31 factors tested, including network and alien properties, we find that aliens with high foraging efficiency are the most successful invaders. Networks exhibiting high alien–native diet overlap, fraction of alien-visited plant species, most-generalist plant connectivity, and number of specialist pollinator species are the most impacted by invaders. Our results mimic several disparate observations conducted in the field and potentially elucidate the mechanisms responsible for their variability.The role of adaptive foraging in the threat of invasive pollinators to plant-pollinator systems is difficult to characterise. Here, Valdavinos et al. use network modelling to show the importance of foraging efficiency, diet overlap, plant species visitation, and degree of specialism in native pollinators.

Chapter 10 Computer Aided Search for Optimal Self-Assembly Systems

Plant–pollinator systems are essential for ecosystem functioning, which calls for an understanding of the determinants of their robustness to environmental threats. Previous studies considering such robustness have focused mostly on species’ connectivity properties, particularly their degree. We hypothesized that species’ phenological attributes are at least as important as degree as determinants of network robustness. To test this, we combined dynamic modeling, computer simulation and analysis of data from 12 plant–pollinator networks with detailed information of topology of interactions as well as species’ phenology of plant flowering and pollinator emergence. We found that phenological attributes are strong determinants of network robustness, a result consistent across the networks studied. Plant species persistence was most sensitive to increased larval mortality of pollinators that start earlier or finish later in the season. Pollinator persistence was especially sensitive to decreased visitation rates and increased larval mortality of specialists. Our findings suggest that seasonality of climatic events and anthropic impacts such as the release of pollutants is critical for the future integrity of terrestrial biodiversity.

Adaptive foraging allows the maintenance of biodiversity of pollination networks

In the broadcast version of the congested clique model, n nodes communicate in synchronous rounds by writing Ologn-bit messages on a whiteboard, which is visible to all of them. The joint input to the nodes is an undirected n-node graph G, with node i receiving the list of its neighbors in G. Our goal is to design a protocol at the end of which the information contained in the whiteboard is enough for reconstructing G. It has already been shown that there is a one-round protocol for reconstructing graphs with bounded degeneracy. The main drawback of that protocol is that the degeneracy m of the input graph G must be known a priori by the nodes. Moreover, the protocol fails when applied to graphs with degeneracy larger than m. In this article, we address this issue by looking for robust reconstruction protocols, that is, protocols which always give the correct answer and work efficiently when the input is restricted to a certain class. We introduce a very simple, two-round protocol that we call Robust-Reconstruction. We prove that this protocol is robust for reconstructing the class of Barabasi-Albert trees with expected message size Ologn. Moreover, we present computational evidence suggesting that Robust-Reconstruction also generates logarithmic size messages for arbitrary Barabasi-Albert networks. Finally, we stress the importance of the preferential attachment mechanism used in the construction of Barabasi-Albert networks by proving that Robust-Reconstructiondoes not generate short messages for random recursive trees.